Essays on Insurance Management - University of St. …...Essays on Insurance Management — The Theory of Insurance Fraud and Empirical Analyses of Auditing Strategies and Cat Bond

Essays on Insurance Management— The Theory of Insurance Fraud and Empirical Analyses

of Auditing Strategies and Cat Bond Investments —

DISSERTATIONof the University of St.Gallen,

School of Management,Economics, Law, Social Sciences

and International Affairsto obtain the title of

Doctor of Philosophy in Management

submitted by

Katja Muller

from

Germany

Approved on the application of

Prof. Dr. Hato Schmeiser

and

Prof. Dr. Martin Eling

Dissertation no. 4164

epubli GmbH, Berlin 2013

The University of St.Gallen, School of Management, Economics, Law,

Social Sciences and International Affairs hereby consents to the printing

of the present dissertation, without hereby expressing any opinion on the

views herein expressed.

St. Gallen, May 17, 2013

The President:

Prof. Dr. Thomas Bieger

To my dear parents/ Za Mama i Tati

Valentina & Matthias

Acknowledgments

I would like to seize the opportunity to express my deepest gratitude to

a number of people who have accompanied me along the way with their

continuous support and encouragement.

To begin with, I would like to sincerely thank my supervisor, Prof.

Dr. Hato Schmeiser, for his generous support and guidance throughout

the development of this thesis and for creating an inspiring research en-

vironment at the Institute of Insurance Economics. I am also grateful

to my co-supervisor, Prof. Dr. Martin Eling, for his interest in my dis-

sertation. Moreover, I am grateful to my co-authors, my colleagues and

my dear friends - Carin, Caroline, Joel, Tobias - for our collaborations

and discussions, and for making my time in St. Gallen an unforgettable

experience.

With all my heart, I would like to thank my parents and my brother

for their never-ending support and unconditional love and care. My

achievements would not have been possible without the generosity and

unwearying care of my dear parents, to whom I owe so much.

St. Gallen, July 2013 Katja Muller

Vorwort

Mein aufrichtiger Dank gilt einer Reihe von Personen, die mich wahrend

der Entstehungsphase dieser Dissertation kontinuierlich unterstutzt und

gefordert haben.

Zunachst mochte ich mich bei meinem Referenten und Doktorvater,

Prof. Dr. Hato Schmeiser, fur seine wertvolle Unterstutzung und fur das

exzellente Arbeitsumfeld am Institut fur Versicherungswirtschaft bedan-

ken. Ausserdem danke ich meinem Korreferenten Prof. Dr. Martin Eling

fur sein Interesse an meiner Dissertation. Ferner bin ich meinen Koauto-

ren, Kollegen und Freunden - Carin, Caroline, Joel, Tobias - fur unsere

gemeinsame Zusammenarbeit und die unvergessliche Zeit in St. Gallen

sehr dankbar.

Von ganzem Herzen mochte ich meinen Eltern und meinem Bruder

fur ihre unablassige Unterstutzung und ihre bedingungslose Liebe und

Zuwendung danken. Das Erreichte ware ohne die Grosszugigkeit und

unermudliche Fursorge meiner lieben Eltern, denen ich so vieles zu ver-

danken habe, nicht moglich gewesen.

Blagodar� vi ot c�loto si sьrce!

St. Gallen, im Juli 2013 Katja Muller

Outline iii

Outline

I Insurance Claims Fraud:Optimal Auditing Strategies in InsuranceCompanies 1

II The Impact of Auditing Strategies onInsurers’ Profitability 41

III The Identification of Insurance Fraud:An Empirical Analysis 85

IV What Drives Insurers’ Demand for CatBond Investments? Evidence from a Pan-European Survey 127

Curriculum Vitae 177

iv Contents

Contents

Contents iv

List of Figures vii

List of Tables viii

Introduction ix

Einfuhrung xiii

I Insurance Claims Fraud:Optimal Auditing Strategies in InsuranceCompanies 1

1 Introduction 2

2 Model Framework 62.1 Optimization of Positions . . . . . . . . . . . . . . . . . 112.2 Assumptions About the Distribution of Information . . . 122.3 Analytical Results . . . . . . . . . . . . . . . . . . . . . . 13

3 Computational Aspects 17

4 Simulation Results 214.1 Reference Setting . . . . . . . . . . . . . . . . . . . . . . 224.2 Sensitivity Analysis of Relevant Parameters . . . . . . . 25

5 Conclusive Remarks 30

6 Appendix 33

References 37

II The Impact of Auditing Strategies onInsurers’ Profitability 41

1 Introduction 42

2 Model Framework and Stakeholders’ Positions 482.1 Optimization Problem . . . . . . . . . . . . . . . . . . . 55

3 Optimal Auditing Strategies 553.1 Policyholder Claiming Scheme . . . . . . . . . . . . . . . 553.2 Insurance Company Auditing Strategy . . . . . . . . . . 58

Contents v

3.3 Behavioral Adaptation . . . . . . . . . . . . . . . . . . . 603.4 Numerical Implementation of Iterative Optimization . . 63

4 Simulation Results 664.1 Parametrization of the Reference Setting . . . . . . . . . 664.2 Simulation Results and Sensitivity Analyses . . . . . . . 67

4.2.1 Development of Optimization Results OverSeveral Iterations . . . . . . . . . . . . . . . . . . . 68

4.2.2 Sensitivity Analyses . . . . . . . . . . . . . . . . . 72

5 Critical Discussion 77

6 Conclusion 79

References 81

III The Identification of Insurance Fraud:An Empirical Analysis 85

1 Introduction 86

2 Theory and Hypotheses Development 912.1 Development of Hypotheses . . . . . . . . . . . . . . . . 912.2 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . 962.3 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . 982.4 Model Derivation . . . . . . . . . . . . . . . . . . . . . . 102

3 Empirical Results 1033.1 Logistic Regression Results . . . . . . . . . . . . . . . . . 1043.2 Special Focus on Loss Amount . . . . . . . . . . . . . . . 111

4 Conclusion and Critical Discussion 114

5 Appendix 117

References 122

IV What Drives Insurers’ Demand for CatBond Investments? Evidence from a Pan-European Survey 127

1 Introduction 128

vi Contents

2 The Demand for Cat Bonds 1322.1 Current Market Size and Investor Base . . . . . . . . . . 1322.2 Development of Hypotheses . . . . . . . . . . . . . . . . 133

3 Data and Methodology 1373.1 Development of Measures . . . . . . . . . . . . . . . . . 1373.2 Participant Recruitment . . . . . . . . . . . . . . . . . . 1383.3 Sample Characteristics and Imputation . . . . . . . . . . 1383.4 Exploratory Factor Analysis . . . . . . . . . . . . . . . . 1393.5 Logistic Regression Model . . . . . . . . . . . . . . . . . 140

4 Empirical Results 1424.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . 1424.2 Determinants of the Cat Bond Investment Decision . . . 1504.3 Further Qualitative Results . . . . . . . . . . . . . . . . 159

5 Summary and Conclusion 165

6 Appendix 1676.1 Aspects Encouraging Cat Bond Investments . . . . . . . 1676.2 Aspects Opposing Cat Bond Investments . . . . . . . . . 1686.3 Further Comments . . . . . . . . . . . . . . . . . . . . . 170

References 172


List of Figures vii

List of Figures

Optimal Auditing Strategies in InsuranceCompanies

1 Acceptance Range from both Stakeholders’ Perspectives . 222 Acceptance Range for Different Risk Aversion Parameters 263 Acceptance Range for Different Fraud Amounts . . . . . . 264 Acceptance Range for Different Insurance Premiums . . . 285 Acceptance Range for Different Costs Per Audit . . . . . 29

Impact of Auditing Strategies on Insurers’Profitability

6 Overview of the Processes Associated with the Filingand Handling of Insurance Claims . . . . . . . . . . . . . 50

7 Interaction between Insurance Company and Policyholders 628 Development of the Optimal Auditing Strategy . . . . . . 699 Development of the Number of Audits and the Number

of Fraudulent Claims . . . . . . . . . . . . . . . . . . . . . 7010 Development of the Insurance Company’s Net Present

Value and the Policyholders’ Gain in Utility . . . . . . . . 7111 Auditing Range and Objective Quantities Depending

on Cost Per Audit . . . . . . . . . . . . . . . . . . . . . . 7312 Auditing Range and Objective Quantities Depending

on Relative Fraud Amount . . . . . . . . . . . . . . . . . . 7413 Auditing Range and Objective Quantities Depending

on Policyholder’s Initial Threshold Value . . . . . . . . . . 7614 Auditing Range Including an Additional Auditing Thresh-

old . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Empirical Analysis of Insurance Fraud15 Contribution of Loss Amount to Predicting the Likeli-

hood of Fraud . . . . . . . . . . . . . . . . . . . . . . . . . 112

viii List of Tables

List of Tables

Optimal Auditing Strategies in InsuranceCompanies

1 Input Parameters for the Reference Setting . . . . . . . . 21

Impact of Auditing Strategies on Insurers’Profitability

2 Input Parameters for the Reference Setting . . . . . . . . 68

Empirical Analysis of Insurance Fraud3 Descriptive Statistics for the Sample Composition I . . . . 994 Descriptive Statistics for the Sample Composition II . . . 1015 Logistic Regression Results Model 1 . . . . . . . . . . . . 1046 Logistic Regression Results Model 2 . . . . . . . . . . . . 1057 Logistic Regression Results Model 3 . . . . . . . . . . . . 1078 Logistic Regression Results Model 4 . . . . . . . . . . . . 1089 Likelihood Ratio Tests for the Models . . . . . . . . . . . 11010 Classification Table for Full Model . . . . . . . . . . . . . 11111 Explanatory Variables Used in the Models . . . . . . . . . 11712 Variance Inflation Factors for All Explanatory Variables . 11813 Descriptive Statistics for the Whole Sample I . . . . . . . 11914 Descriptive Statistics for the Whole Sample II . . . . . . . 120

Drivers of Cat Bond Investments15 Sample Composition . . . . . . . . . . . . . . . . . . . . . 14416 Descriptive Statistics for the Company Sizes . . . . . . . . 14717 Mann-Whitney U Test . . . . . . . . . . . . . . . . . . . . 14818 Potential Determinants of the Investment Decision . . . . 14919 Rotated Factor Loadings Matrix with Additional Statistics 15220 Logistic Regression with all Potential Determinants . . . . 15521 Classification Table for Model with all Potential Deter-

minants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15722 Logistic Regression with Significant Determinants . . . . . 15823 Classification Table for Model with Significant Determinants15924 Open Questions . . . . . . . . . . . . . . . . . . . . . . . . 160

Introduction ix

Introduction

The phenomenon of insurance fraud is usually met with an ambivalent

attitude as few individuals perceive insurance fraud as a white-collar

crime. At the same time, however, many are appalled by the ruthless ac-

tions undertaken to scam excessive indemnity payments at the expense

of the entire policyholder population. From the insurance company per-

spective, fraud represents a major challenge which has existed for many

years. It can be observed in all classes of insurance and results in a large

amount of excess payments each year. In this doctoral thesis, two out of

the overall four research papers focus on one particular aspect of insur-

ance economics: developing theoretical models to derive approaches on

how to tackle different challenges related to insurance fraud.

The first paper, “Insurance Claims Fraud: Optimal Auditing Strate-

gies in Insurance Companies”, presents a theoretical model framework

for determining conditions under which both the insurance company and

the policyholder are willing to enter into a relationship. Assuming that

fraud is indeed present, the aim is to derive an agreement range con-

sisting of all auditing and defrauding strategy combinations that all

stakeholders are inclined to accept. Hereby, the behavioral strategies

are characterized by the probability of performing an audit or engaging

in fraudulent activities respectively. Our findings show that the num-

ber of all valid constructs strongly depends on parameters like insurance

premiums or the cost per audit. For a final statement with regard to op-

timality, however, it is necessary to take the participants’ market power

into consideration.

The following paper, entitled “The Impact of Auditing Strategies on

Insurers’ Profitability” alters the aspect of agreement and addresses the

question of how to optimally configure the auditing strategy from the

insurance company perspective. While the aim is to maximize the in-

surer’s objective quantity, we still take the policyholder perspective into

consideration to ensure a willingness to adhere to the insurance relation-

ship. Our results evolve around optimal auditing strategies in the form

x Introduction

of ranges triggered by the magnitude of a filed claim. Furthermore, we

allow for both stakeholders to adapt their behavior by picking up market

signals. One of our key findings shows that, against all expectations, it

is actually not favorable to try and anticipate the supposedly prevalent

auditing strategy from the policyholder point of view.

In connection with our studies, we were given the opportunity to

conduct numerous interviews with industry experts from different fraud

investigation divisions. In summary, they all agree on the severity of this

matter and collectively call for necessary actions to be taken. This disser-

tation provides a thorough insight into the characteristics and challenges

associated with insurance fraud and can help to implement appropriate

measures for handling it more effectively in insurance companies.

While the first part of the dissertation evolves around theoretical

frameworks, we set our focus on the analysis of insurance markets in the

second part. Founded by the increasing availability of data throughout

the last decades, empirical research has advanced to become a sought-

after approach in the field of insurance economics. It complements theo-

rectical models and can help to promote a deeper understanding for the

underlying processes. With regard to behavioral patterns and decision-

making, empirical research provides a wide range of methods for unveil-

ing potential indicators and drivers. Based on this line of reasoning, the

remaining two research papers of this dissertation pertain to the area of

empirical research in the context of insurance markets.

The first paper of this dissertation in the context of market analyses

is entitled “The Identification of Insurance Fraud - An Empirical Analy-

sis”. It is an empirical analysis of potential fraud indicators with a focus

on the automobile sector. Based on a comprehensive data sample from

a Swiss insurance company, we identify characteristics which allow for

a distinction between legitimate and illegitimate incoming claims. The

set of significant determinants comprises variables on the policyholder,

vehicle, policy and loss level. Based on our findings, we are able to draw

a profile which identifies fraud-prone policyholders as middle-aged indi-

Introduction xi

viduals having a good driving record and owning high-valued vehicles.

It seems worth mentioning that the option to cheat on one’s insurance

company is solely taken into consideration in the case of small- and

medium-sized losses. These results indicate that individuals try to an-

ticipate the supposed auditing strategy to hopefully remain undetected.

Finally, the second paper in the center of empiricism “What Drives

Insurers’ Demand for Cat Bond Investments? Evidence from a Pan-

European Survey” addresses the issue of low demand in cat bond in-

vestments from the insurance and reinsurance company perspective in

Europe. Despite the asset class’ attractive risk-return profile and diversi-

fication potential, insurers account for merely ten percent of the current

demand in the market, raising the question as to how this observation

may be explained. Our comprehensive study reveals that the firm’s ex-

perience and expertise related to cat bonds, their perceived fit with the

asset and liability management goals as well as the prevailing regulatory

regime have a significant impact on the companies’ decision whether or

not to invest in this particular asset class. The results seem to be of high

relevance, particularly for practitioners and regulators, and can support

further growth of this still relatively small segment of the capital markets.

Founded on a broad data base, the last two research papers of this

thesis uncover main indicators for fraudulent behaviour and drivers in

the decision-making process of insurance companies related to cat bonds.

The results are not only of interest to practitioners, but also provide new

insights which may help to advance theoretical models.

Einfuhrung xiii

Einfuhrung

Ansichten zum Thema Versicherungsbetrug sind stark divergierender Na-

tur. Nicht wenige sehen darin einen Kavaliersdelikt oder eine Gelegen-

heit, vergangene Pramienzahlungen zusatzlich zu kompensieren. Demge-

genuber wird die Rucksichtslosigkeit von vielen verurteilt - insbesondere

basierend auf der Erkenntnis, dass die einhergehenden Zahlungen von

der Gesamtheit aller Versicherungsnehmer getragen werden. Aus Sicht

der Unternehmen ist Versicherungsbetrug eine der zentralen Herausfor-

derungen. Betrugsversuche sind in fast allen Versicherungssparten zu

finden und haben jedes Jahr erhebliche Zahlungen zur Folge. In der vor-

liegenden Dissertation sind zwei der insgesamt vier Forschungsarbeiten

dieser Thematik gewidmet. Unser Bestreben ist es, mit Hilfe theoreti-

scher Modellrahmen, Empfehlungen zum Umgang mit Betrugsfallen und

-versuchen herzuleiten.

Die erste Forschungsarbeit mit dem Titel “Insurance Claims Fraud:

Optimal Auditing Strategies in Insurance Companies” hat zum Ziel, Kon-

ditionen herzuleiten und zu analysieren, unter denen sowohl Unterneh-

men als auch Versicherungsnehmer grundsatzlich bereit sind, ein Ver-

tragsverhaltnis miteinander einzugehen. Hierzu betrachten wir aus Sicht

des Versicherungsunternehmens die Wahrscheinlichkeit, ein Prufverfahren

einzuleiten, wahrend bei den Versicherungsnehmern die Betrugswahr-

scheinlichkeit einbezogen wird. Unter der Annahme, dass Betrug tatsach-

lich stattfindet, werden diejenigen Verhaltenskombinationen ermittelt,

die beide Teilnehmer jeweils gewillt sind zu akzeptieren. Unsere Ergeb-

nisse zeigen, dass die Auspragung dieses Einigungsbereiches insbesondere

von der Wahl der Parameter Pramienhohe und Prufkosten abhangt. Ei-

ne abschliessende Bewertung mit Blick auf eine Gleichgewichtssituation

ist lediglich unter Hinzunahme der Markmacht der Parteien moglich.

In der zweiten Arbeit “The Impact of Auditing Strategies on Insurers’

Profitability” verabschieden wir uns von der Zielsetzung einer Einigung,

und untersuchen die Konfiguration optimaler Kontrollstrategien. Dazu

versetzen wir uns in die Lage des Versicherungsunternehmens, unter

xiv Einfuhrung

Berucksichtigung der Teilnahmebedingungen des Versicherten. Die resul-

tierenden Prufstrategien indizieren, ob ausgehend von der Schadenhohe

eine Uberprufung eingeleitet oder die Meldung direkt abgewickelt werden

soll. Zusatzlich erweitern wir unser Modell um die Option einer kontinu-

ierlichen Verhaltensanpassung beider Parteien. Es stellt sich heraus, dass

es fur den Versicherungsnehmer entgegen der Intuition unvorteilhaft ist,

das vermutete Kontrollverhalten des Versicherers zu antizipieren.

Im Zuge unserer Forschung hatten wir mehrfach die Gelegenheit, In-

terviews mit Versicherungsexperten aus dem Bereich der Betrugsbekamp-

fung zu fuhren. Zusammenfassend kann gesagt werden, dass angesichts

der umfassenden Prasenz und der wirtschaftlichen Implikationen, adaqua-

te Losungen fur den effektiven Umgang mit Versicherungsbetrug immer

wichtiger werden. Der erste Teil dieser Dissertation gewahrt einen um-

fassenden Einblick sowohl in die Thematik als auch die einhergehenden

Herausforderungen und legt Vorschlage fur geeignete Massnahmen dar.

In Erganzung zu den modelltheoretischen Ansatzen der ersten beiden

Forschungsarbeiten ist der zweite Teil der Dissertation der empirischen

Analyse von Versicherungsmarkten gewidmet. Im Zuge der zunehmen-

den Verfugbarkeit von Daten und Informationen in den vergangenen

Jahrzehnten sind empirische Analysen zu einem zentralen Element der

Forschung im Bereich Versicherungswirtschaft avanciert. Sie sind als Mit-

tel zur Erganzung und Verifizierung theoretischer Modelle zu sehen, und

konnen dazu beitragen, zusatzliche Erkenntnisse uber zugrundeliegende

Prozesse zu gewinnen. Insbesondere mit Blick auf die Erforschung von

Verhaltensmustern und Entscheidungsprozessen bietet die Empirie ein

breites Spektrum von Verfahren und Methoden an.

Bei der ersten empirischen Forschungsarbeit mit dem Titel “The Iden-

tification of Insurance Fraud - An Empirical Analysis” handelt es sich um

eine Analyse von Betrugsindikatoren. Ausgehend von einem umfassenden

Datensatz geprufter Schadenmeldungen aus der Motorfahrzeugversiche-

rung eines grossen Schweizer Versicherers werden Faktoren ermittelt, die

eine eindeutige Abgrenzung zwischen ehrlichen und betrugerischen Mel-

Einfuhrung xv

dungen ermoglichen. Die potenziellen Kriterien sind auf Ebene des Versi-

cherten selbst, dem Motorfahrzeug, der Police sowie der Schadenmeldung

angesiedelt. Unsere Ergebnisse portratieren betrugswillige Versicherungs-

nehmer als Personen mittleren Alters mit einer uberdurchschnittlichen

Anzahl von Schadenfreiheitsjahren und in Besitz von hochpreisigen Fahr-

zeugen. Insbesondere scheinen sie Betrugsversuche lediglich im Falle von

kleinen und mittleren Schaden in Erwagung zu ziehen. Diese Erkennt-

nisse legen die Vermutung nahe, dass Versicherungsnehmer in der Tat

Vermutungen uber die bestehenden Kontrollmechanismen anstellen und

versuchen, diese zu umgehen.

Die zweite Arbeit im Fokus der Empirie widmet sich dem Investitions-

verhalten von Versicherungsunternehmen in Bezug auf Katastrophenan-

leihen. Unter dem Titel “What Drives Insurers’ Demand for Cat Bond

Investments? Evidence from a Pan-European Survey” werden potenti-

elle Entscheidungsfaktoren fur oder gegen diese Anlageklasse ermittelt.

Trotz ihres attraktiven Risiko-Rendite-Profils und Diversifikationspoten-

tials kommen Versicherer lediglich fur zehn Prozent der gesamten Nach-

frage im Markt auf. Dies wirft die Frage nach moglichen Erklarungen

auf. Zu diesem Zweck wurde eine detaillierte Umfrage mit zahlreichen eu-

ropaischen Erst- und Zweitversicherungsunternehmen durchgefuhrt. Die

statistische Auswertung der Angaben zeigt, dass die Faktoren “Erfah-

rung und Expertise” in Bezug auf Katastrophenbonds, deren “Kompa-

tibilitat mit den Assetmanagementzielen” des Unternehmens sowie die

“bestehenden Regulierungsrahmenwerke” einen signifikanten Einfluss auf

die Investmententscheidung haben. Unsere Ergebnisse sind fur Praktiker

und Regulierer von besonderer Relevanz, und konnen dazu beitragen, ak-

tuelle Investitionsbarrieren zu uberwinden.

Ausgehend von einer umfassenden Datengrundlage aus zwei verschie-

denen Bereichen des Versicherungsmanagement werden in den letzten

beiden Forschungsarbeiten Indikatoren fur Betrugsverhalten sowie trei-

bende Faktoren bei der Investitionsentscheidung von Versicherungsunter-

nehmen ermittelt und analysiert. Die Ergebnisse sollten dazu geeignet

xvi Einfuhrung

sein, neue Impulse fur die Weiterentwicklung von theoretischen Modellen

zu geben.

1

Part I

Insurance Claims Fraud:

Optimal Auditing Strategies

in Insurance Companies

Abstract

Insurance claims fraud is one of the major concerns in the insurance in-

dustry. According to many estimates, excess payments due to fraudulent

claims account for a large percentage of the total payments affecting all

classes of insurance. In this study, we develop a model framework based

on a costly state verification setting in which, while policyholders ob-

serve the amount of loss privately, the insurance company can decide to

audit incoming claims at some cost. In particular, optimization prob-

lems are formulated from both stakeholders’ positions considering that

for each of them willing to sign an insurance contract, certain participa-

tion constraints need to be fulfilled. Besides deriving analytical solutions

regarding optimal fraud and auditing strategies, we provide a numerical

approach based on Monte Carlo methods. The simulation results illus-

trate the acceptance range that consists of all valid fraud and auditing

probability combinations both stakeholders are willing to tolerate. We

discuss the impact of different valid probability combinations on the in-

surance company’s and policyholder’s objective quantities respectively

and analyze the sensitivity of the acceptance range with respect to dif-

ferent input parameters. 1

1K. Muller, H. Schmeiser, and J. Wagner. Insurance Claims Fraud: Optimal Au-diting Strategies in Insurance Companies. Working Papers on Risk Management and

Insurance, 2011.This paper has been presented at the Annual Meeting of the Western Risk and In-surance Association in January 2012 and at the Jahrestagung des Deutschen Vereinsfur Versicherungswissenschaft in March 2012.

2 I Theory of Insurance Fraud

1 Introduction

Insurance claims fraud has been one of the major concerns in the in-

surance industry for a long time and has attracted much attention in

both scientific and firm-level environments. There exist many research

papers and studies on the detection and deterrence of fraudulent activ-

ities and the optimal design of insurance contracts (see, e.g., Viaene

and Dedene (2004), Picard (2009), Dionne, Giuliano, and Picard (2009),

GDV (2011)). Despite all efforts, the Association of British Insurers

(2012) reports the uncovering of 139’000 dishonest claims in the UK in

2011 alone, adding up to almost 1 billion in illegitimate loss reports;

the estimated number of unrevealed cases is assumed to be substantially

higher. In this study, we show that with the goal of minimizing insur-

ance companies’ costs, the complete elimination of fraudulent activities

is not always desirable. We derive acceptance ranges that comprise all

valid fraud and auditing probability combinations under which contract

conditions remain attractive enough for both insurer and policyholder

to adhere to the insurance relationship. The actual strategies are chosen

based on the respective market power.

Insurance claims fraud is a multi-layered phenomenon. While it is

often associated with criminal activities, only a minority of illegitimate

claims is said to contain outright fraud (see, e.g., Viaene and Dedene

(2004), Tennyson (2008)). This observation is probably due to the fact

that for a case to be declared criminal fraud it needs to be proven that it

is ”a willful act of obtaining money or value from an insurer under false

pretenses or material misrepresentations” (Derrig (2002)). The more

common and frequent type of insurance claims fraud is referred to as

soft fraud. Even though there exists no clear definition of the term, it

is generally associated with the attempt to exaggerate the magnitude

of an otherwise legitimate claim (see, e.g., Weisberg and Derrig (1991),

Viaene and Dedene (2004), Tennyson (2008)). This form of inflation is

also called build-up. In the context of our study, we use the term insur-

ance claims fraud in the sense of soft fraud or build-up, i.e., fraud-prone

1 Introduction 3

policyholders claiming loss amounts exceeding their actual value.

The appearance of insurance claims fraud is based on information be-

ing asymmetrically distributed between the policyholder and the corre-

sponding insurance company (see, e.g., Derrig (2002)). Since individuals

observe the amount of loss privately after the time of occurrence, they

may decide to misrepresent the magnitude. In a costly state verifica-

tion environment as applied by researchers (see, e.g., Townsend (1979),

Mookherjee and Png (1989), Bond and Crocker (1997) and Picard and

Fagart (1999)), the insurer has the opportunity to perform verification

processes to determine the truthfulness of an incoming claim. Any de-

tected engagement in fraudulent activities can be charged with a penalty

payment. However, since this auditing comes at some cost, the insurance

company has to weigh the benefits against the accompanying expenses.

Another component that needs to be considered in this calculation is the

policyholder perspective. Viaene and Dedene (2004) found that policy-

holders who had negative experiences throughout the insurance relation-

ship such as delayed indemnifications or underpayment were more likely

to engage in fraudulent activities.

While costly state verification is based on the insurance company

being able to detect attempts of misrepresentation, the costly state fal-

sification approach focuses on the policyholder incurring some cost to

manipulate the magnitude of loss such that it becomes unverifiable. The

general setting was introduced by Lacker and Weinberg (1989) and trans-

ferred to the specific features of the insurance environment by Crocker

and Morgan (1998) and Crocker and Tennyson (2002).

A different approach in the fight against insurance claims fraud was

taken by Dionne and Vanasse (1992) and Moreno, Vazquez, and Watt

(2006). Instead of engaging in cost-intensive auditing, the insurance com-

pany raises the insurance premium whenever the policyholder filed some

claim in the previous period. This strategy is often applied in the auto-

mobile insurance sector where contract renewals are a common standard.

As a result, illegitimate claims when no insured loss occurred may be pre-

vented.


In this study, we consider an alternative approach on the subject

of claims handling, especially when fraud is present. For this purpose,

we focus on the parties’ behavioral strategies, i.e., from the insurance

company perspective, we consider the verification scheme. It is char-

acterized by the probability of performing an audit, whereas from the

policyholder point of view, the defrauding strategy is taken into account

as represented by the probability of engaging in fraudulent activities.

The aim is to identify and analyze all conditions under which the in-

surance relationship is attractive for the insurance company and the

policyholder, i.e., both stakeholders are willing to adhere to the insur-

ance contract. Particularly, for any fraud strategy, i.e, the probability of

filing an inflated loss amount, we determine the set containing all valid

corresponding auditing probabilities, given some constant cost per au-

dit and vice versa. With regard to optimality, we can make predictions

based on the stakeholders’ respective market power.

Previous research has focused on deriving optimal contracts such that

at equilibrium, the policyholders have an incentive to always report their

losses truthfully (see, e.g., Townsend (1979), Picard and Fagart (1999)).

However, the question arises as to how the two stakeholders representing

two opposing groups of interest can be brought together in the first place.

Which behavioral patterns, i.e., defrauding and auditing probabilities, is

the respective other willing to accept without being worse off than in the

situation when no insurance contract was signed prior to the occurrence

of loss? From the insurance company perspective, one can assume that,

given some fixed cost per audit, it is not appealing to enter an insurance

relationship with individuals who engage in build-up on a large scale in

terms of frequency and severity. From the policyholder point of view

on the other side, it appears to be intuitive to assume that delayed

or reduced indemnification due to extensive auditing might curtail the

attractiveness of insurance.

Obtaining the resulting set of all acceptable fraud and auditing prob-

ability combinations, we make a crucial observation. In the context

of cost-minimizing insurance companies, a mutual acceptance between

both stakeholders can be reached for any fraudulent behavior the pol-

icyholder might exhibit. In particular, even in the case when the loss

1 Introduction 5

amount is inflated in most of the incoming claims, there may exist audit-

ing strategies such that the insurer is willing to adhere to the insurance

relationship and even be able to optimize its objective quantity. This

result underlines the expectation expressed by Watt (2003) showing that

for cost-minimizing insurance companies it is not necessarily desirable

to undercut all fraudulent activities.

Based on the results of the acceptance range, we analyze all valid

fraud and auditing probability combinations with respect to their opti-

mality for the stakeholders’ respective objective quantities. As expected,

we are able to show that the best possible outcome can never be achieved

for both the insurance company and the policyholder at the same time.

Which one out of all valid behavioral strategy combinations they settle

on, depends on their respective market power.

We want to emphasize that the acceptance range is not to be un-

derstood as a cooperative agreement that both parties decide upon. It

intends to demonstrate the range of all possibilities attractive enough so

that both insurer and policyholder are willing to maintain the insurance

relationship.

The model derived in this study is based on the costly state verifica-

tion environment considering the insurance company’s net present value

of future cash flows and the policyholder’s expected utility of his termi-

nal wealth position. To make sure that both stakeholders are willing to

sign an insurance contract, we include participation constraints. We de-

rive and analyze some analytical solutions to the optimization problems.

Due to the complexity of the model, however, it is not always possible

to obtain closed-form solutions. Therefore, we present a numerical ap-

proach using Monte Carlo methods. The simulation results and their

implications for both stakeholders’ optimal strategies are discussed and

illustrated graphically.

The remainder of this study is organized as follows: we start by

presenting the model framework and first analytical results in Section 2.

Thereafter, the numerical approach and the corresponding program are


introduced in Section 3. In Section 4, we discuss the simulation results

before concluding in Section 5.

2 Model Framework

An individual with initial wealth W0 is offered the possibility to sign an

insurance contract with a fixed premium P due by the time of inception

of insurance coverage in t = t0. At the same time, he faces some un-

certain loss θ of stochastic amount which, by the time of occurrence, is

observed privately. In case he signed the insurance contract earlier, the

policyholder can then chose to file a claim of some size θ. In the case

of honest behavior, the amount of that claim will equal the actual loss,

i.e., θ = θ. If the policyholder decides to commit fraud, he reports some

finite θ > θ. The probability of the policyholder choosing to report a

fraudulent claim is denoted by p.

The insurer on the other hand has no information about the actual

occurred loss. He therefore audits incoming claims with some probability

q and at the constant cost of k per audited claim. Depending on whether

auditing took place or not and the outcome in case of an audit, a payment

R is made from the insurance company to the policyholder. Considering

the different possible combinations of fraud and auditing probabilities p

and q, the payment R can be defined as follows:

R(θ, θ) = (1 − p) θ + p [(1 − q) θ + q (θ −B)], (1)

with B being the penalty payment deducted from the claim amount θ.

Equation (1) can be interpreted as an indemnity payment if R is

positive, whereas a negative R represents the payment made from the

insured to the insurance company in case of detected fraud when B > θ.

There are several possible cases: if the reported loss is not checked, the

insured receives the payment of θ. In the case of auditing, the payment

depends on whether the policyholder committed fraud or not. Proven

honesty leads to a payment of θ = θ. If a misrepresentation of loss is

determined, the policyholder faces some penalty B. In practice, B is

mostly chosen such that θ −B = 0.

2 Model Framework 7

In this setting, we take audits to be perfect, i.e., if a fraudulent claim

is made, it will surely be detected in the case of auditing.

In the following, we introduce the setting as well as the objective

quantity and the participation constraint from the insurance company

perspective. The same is done from the policyholder point of view.

Based on this information, we state the resulting optimization problems

for both stakeholders in Section 2.1. Assumptions about the distribution

of information among the policyholder and the insurance company are

given in Section 2.2 before presenting analytical results in Section 2.3.

Insurance Company: Cash Flow, Net Present Value,

Participation Constraint

In the framework introduced above, we observe the future cash flows

from the insurance company perspective at the time of insurance incep-

tion in t = t0 and the time of loss realization and settling in t = t1 and

analyze their resulting present value.

In the case of an insurance contract coming into existence, the insur-

ance company receives the premium payment P in t = t0. An incoming

claim in t = t1 that is audited with probability q and at some given cost

k(> 0) per analyzed claim, results in −R(θ, θ) − qk.

The insurance company’s net present value of its future incoming and

outgoing cash flows is denoted by

NPV = P − E(R(θ, θ)) − qk, 2 (2)

where R(θ, θ) denotes the indemnity payment as defined in (1).

Condition 1 The insurance company is willing to participate in an in-

surance contract if its net present value is positive. Hence, one obtains

the following participation constraint:

2We consider the expected value of future cash flows discounted with the risk-freeinterest rate rf = 0.


NPV ≥ 0. (3)

Applying Equation (2), participation constraint (3) can be formu-

lated as

P ≥ E(R(θ, θ)) + qk. (4)

Apparently, the expression on the right-hand side represents a lower

bound for the premium payments the insurance company is willing to

accept. Its value depends on the expected value of the indemnity pay-

ments that will be made and a loading that reflects the auditing effort.

Policyholder: Wealth Position, Utility Function,


From the policyholder perspective, we analyze his wealth position and

the corresponding expected utility at the time of inception of insurance

cover t = t0 and the time of loss realization and claiming t = t1 for the

framework introduced above.

An individual initially owns some wealth W0. Its consecutive devel-

opment depends on whether he signs an insurance contract prior to the

occurrence of loss or not. In a situation without an insurance contract,

the individual holds the unchanged wealth position:

WB0 = W0 (5)

at time t = t0. At the time of loss occurrence in t = t1, this amount

decreases to:

WB1 = WB

0 − θ = W0 − θ. (6)

The decision to sign an insurance contract is accompanied by the

payment of an insurance premium P . Consequently, when signing the

contract at time t = t0, the individual owns the wealth position:

2 Model Framework 9

WA0 = W0 − P. (7)

Assuming a loss θ of some stochastic level occurs and therefore a

claim is filed at time t = t1 , the policyholder’s wealth at that point in

time is denoted by:

WA1 = WA

0 − θ + R(θ, θ) = W0 − P − θ + R(θ, θ) (8)

with R(θ, θ) as defined in (1).

We assume the policyholder’s utility being described by a standard

mean-variance utility function of his individual wealth. For a given

wealth position W and the risk aversion parameter a(≥ 0) of the in-

dividual, this utility function is given by

U(W ) = E(W ) −a

2Var(W ), (9)

where E(W ) denotes the expected value of the stochastic variable W .

In the case where no insurance contract was signed prior to the oc-

currence of loss, using Equation (6) and definition (9) the final utility is

written as:

U(WB1 ) = E(W0 − θ) −

a

2Var(W0 − θ)

= W0 − E(θ) −a

2Var(θ). (10)

For the setting in which an insurance contract was signed by applying

the definition in (9) to Equation (8), we obtain:

U(WA1 ) = E(W0 − P − θ + R(θ, θ)) −

a

2Var(W0 − P − θ + R(θ, θ))

= W0 − P − E(θ −R(θ, θ)) −a

2Var(θ −R(θ, θ)). (11)

Comparing Equations (10) and (11), one sees the difference in in-

fluencing factors for the final expected utility for each situation. In a


setting without the existence of an insurance contract, the final expected

utility U(WB1 ) solely depends on the extend of the actual loss θ and the

policyholder’s risk aversion parameter a. However in a situation in which

insurance coverage exists, the value of the corresponding expected utility

U(WA1 ) is not only influenced by θ, P and a. In addition, the policy-

holder’s fraud strategy p and the insurer’s auditing strategy q have an

impact on that value due to the payment of R (see (1)). Moreover, if the

insured decides to commit fraud, the size of θ that he chooses to claim

is relevant as well as the enforced penalty payment B (see (1)) in case

the fraudulent claim gets detected.

Condition 2 The individual’s decision to get insurance coverage in the

first place depends on whether his utility by the time of loss occurrence

is greater with having insurance than without it. In other words:

U(WA1 ) ≥ U(WB

1 ). (12)

Using (11) and (10) this participation constraint (12) can be written

as:

−P + E(R(θ, θ)) −a

2Var(θ −R(θ, θ)) ≥ −

a

2Var(θ)

⇐⇒ P − E(R(θ, θ)) ≤ −a

2Var(R(θ, θ)) + aCov(θ,R(θ, θ)). (13)

Based on the representation

P ≤ E(R(θ, θ)) −a

2Var(R(θ, θ)) + a Cov (θ,R(θ, θ)),

the inequality in (13) can be interpreted as an upper bound for the

insurance premium the potential policyholder is willing to pay for his

insurance coverage. It depends on the utility of the payment R and the

covariance between actual loss θ and R. Furthermore, the individual’s

risk aversion parameter a has an influence on his willingness to pay.

2.1 Optimization of Positions 11

2.1 Optimization of Positions

So far, the model framework and the participation constraints for both

the policyholder and the insurance company have been presented. Based

on this information, we state the corresponding optimization problems.

The insurance company is aiming to maximize the net present value

of the incoming and outgoing future payments with respect to its au-

dit strategy such that both stakeholders are still willing to participate,

i.e., Equations (12) and (3) hold. Again, it is assumed that the other

parameters are given. This objective function can be written as:

Insurance Company’s Optimization Problem

Find the optimal audit strategy q s.t. NPV is maximized

and Equations (12), (3) hold.

(14)

At the same time, the policyholder’s aim is to maximize his final

expected utility with respect to his fraud strategy such that both partic-

ipation constraints (12) and (3) hold, i.e., an insurance contract exists.

It is assumed that all the other parameters are given. We will denote

this optimization problem by:

Policyholder’s Optimization Problem

Find the optimal fraud behavior p s.t. U(WA1 ) is maximized

and Equations (12), (3) hold.

(15)

Both stakeholders try to optimize their own respective position. Our

aim is to analyze these conflicting objectives and participation constraints

from both the insured’s and insurer’s perspective and find a common ac-

ceptance range for the resulting fraud and auditing strategies.


2.2 Assumptions About the Distribution of

Information

Before presenting the results of our analytical analyses, we summarize

the assumptions regarding the distribution of information among the

stakeholders.

Insurance Company Perspective

The choice of the insurance company’s feasible auditing strategies de-

pends on the policyholder’s prevalent defrauding behavior, i.e., the po-

tential fraud amount and the probability of an incoming claim to be in-

flated. The insurance company is assumed to have full information about

the distribution of the reported losses θ due to having observed incoming

claims to date. In particular, this information can be specified for each

insurance segment or even loss type. Furthermore, we expect that it has

an adequate estimate for the distribution of the actual losses θ based on

the outcomes of previous auditing processes. Consequently, the insurer is

able to deduce the deviation from the magnitude that is to be expected

for the particular loss type α := θ/θ, i.e., the potential fraud amount

in case fraudulent behavior occurs. Since the optimal auditing strategy

also depends on the second component of the policyholder’s defrauding

strategy, the prevalent fraud probability p, the insurance company has

to estimate this value as well. For this purpose, whole catalogs consist-

ing of criteria, so-called red flags, have been derived and implemented

aiming to estimate the probability of a claim being illegitimate as accu-

rately as possible (see, e.g., Belhadji, Dionne, and Tarkhani (2000) and

Bermudez, Perez, Ayuso, Gomez, and Vazquez (2008)). Such indicators

can be targeted at the individuals’ characteristics itself like gender, na-

tionality or place of residence as well as the attributes associated with

the loss event. Combining this information, one is able to obtain a pre-

cise predictor for the fraud probability p (see, e.g., Dionne, Giuliano,

and Picard (2009)). It then chooses the corresponding optimal audit

probability that maximizes its NPV in response.

2.3 Analytical Results 13

Policyholder Perspective

We assume that fraud-prone policyholders do not have sufficient infor-

mation about the insurance company’s auditing process itself, i.e., he or

she does not know the exact criteria for a claim to undergo verification.

As a consequence, the individual cannot manipulate the claim in a way

such that the insurer would not be able to identify the fraud attempt.

This assumption is essential and not unrealistic. Waiving it would make

auditing of any kind redundant since the insurance company would never

be able to detect loss inflation or other kinds of manipulation regardless

of how the verification process is designed.

For the purpose of our analysis, we assume the policyholder to be

able to estimate the probability of being audited by the insurance com-

pany when submitting a claim. This assumption is not in conflict with

the one made before. The knowledge of the probability of one’s claim

being audited does not imply an ability to manipulate the verifiability.

Rather, it provides the policyholder with the possibility to become aware

of which fraud behavior is advantageous in this particular situation and

maybe choose the optimal one.

In the context of our study, we consider one observation period and

determine all potentially feasible behavioral strategies from both the in-

surance company and the policyholder perspectives. Based on their de-

cisions, however, other behavioral strategies may become more favorable

for one or the other party in the consecutive periods. Therefore, the po-

tential behavioral options need to be reconsidered by both stakeholders

at the beginning of each observation period.

2.3 Analytical Results

In the course of this subsection, we derive analytical results for the pre-

sented optimization problems assuming different conditions. The proofs

can be found in the Appendix.

In the first proposition, we derive optimal fraud and auditing strate-

gies p and q for a special setting of the model framework. The crucial


assumption in this case is concerning the policyholder’s risk aversion

parameter a that is set a = 0, i.e., we assume the policyholder to be risk-

neutral. This implies optimizing the insured’s objective function from a

present value perspective.

Proposition 1 For a = 0 and θ, θ such that 0 ≤ θ < θ, the optimal

fraud and auditing strategies from both stakeholders perspectives’ are p =

1 and q = 0. This results in P = E(θ).

This proposition implies that under the given assumptions, the insur-

ance company should waive auditing incoming claims and allow fraudu-

lent behavior instead. In return, the expected amount of fraud will be

added to the insurance premium. Furthermore, the proposition confirms

a characteristic behavior that risk-neutral policyholders show. They are

assumed to have no interest in insuring a potential loss at a premium

which exceeds its expected value.3 Since in this specific setting, all policy-

holders claim the fraudulent amount θ at all times, the premium cannot

be set higher than the expected value of θ. On the other hand, for the

insurance company to be willing to participate in the insurance rela-

tionship, this premium cannot deceed this value. Hence, the insurance

premium equals exactly E(θ).

In the remainder of this subsection, optimal fraud and auditing strate-

gies will be derived for the policyholder and insurance company respec-

tively in a more general setting. First of all, the policyholder is assumed

to be risk-averse, i.e., the risk aversion parameter a is strictly positive,

a > 0. This means his objective function is actually given as an expected

utility function, i.e., the variance of the difference between indemnity

payment R(θ, θ) and actual loss θ, denoted by Var(θ − R(θ, θ)), has an

impact on the final result.

Furthermore, whenever the policyholder decides to make a fraudulent

claim, he reports θ = αθ for some given finite α ≥ 1 to the insurance

company. This setting implies that the relative amount of fraud is con-

stant. We deem it likely to assume that fraud-prone policyholders take

the actual loss amount into consideration when trying to inflate it, i.e.,

3See, e.g., Kirstein (2000).

2.3 Analytical Results 15

they regard the relative fraud amount as a percentage surcharge. In

this way, the filed claim does not deviate substantially from the loss

amounts that can be expected related to the corresponding loss type.

Consequently, the inflated claim is not perceived as illegitimate by the

insurance company which makes it less probable to undergo verification.

This assumption is in line with the observations stated by Viaene and

Dedene (2004). They found that in the context of soft fraud, the excess

amounts tend to be relatively small.

We will derive optimal fraud and auditing strategies, namely popt

and qopt, for the setting introduced above. Other than in Proposition 1,

the potential policyholder is assumed to be risk-averse.

Proposition 2 Assume p, q to be in the acceptance range, i.e., an in-

surance contract exists. For a > 0, B = θ, θ = αθ with some given

α ≥ 1, the respective optimal strategies popt, qopt are given by:

(i) Insurance company perspective

Let some p be given. In order for the net present value NPV to be

maximized, choose

qopt =

{

as large as possible if p > p∗

as small as possible if p ≤ p∗, (16)

where p∗ :=k

αE(θ).

(ii) Policyholder perspective

Let some q be given. In order for the final expected utility U(WA1 )

to be maximized, choose

popt =

as large as possible s.t. −E(θ)ap(1−α(1−q)) Var(θ) ≥ 1

as small as possible s.t. −E(θ)ap(1−α(1−q)) Var(θ) ≤ 0

. (17)


For the case 0 < −E(θ)ap(1−α(1−q)) Var(θ) < 1 no general statement can

be made.

Proposition 2(i) looks at the optimization problem from the insur-

ance company perspective. It states the optimal auditing strategy with

respect to a given fraud probability. The insurance company has two

general strategies to choose from. It can either decide to audit the in-

coming claims with the maximal probability possible, i.e., such that the

participation constraints of both policyholder and insurance company

hold true, or the auditing probability can be chosen as small as possible.

This decision depends on an estimate of the policyholder’s behavior p.

Based on whether it exceeds or deceeds the threshold kαE(θ) , the insur-

ance company opts for a high or low auditing probability respectively.

According to Proposition 2(i), the exceed of the threshold is influenced

by the costs per audit k. The lower these are, given some fixed α and

θ, the more likely it is for the fraud probability to exceed the resulting

threshold. In this case, it becomes optimal for the insurance company

to verify the incoming claims with a high probability. The opposite re-

lationship holds true for the expected loss amount θ and the degree of

fraud that is represented by α. The higher their values are, the lower

the threshold becomes and the more likely it is for the estimated fraud

probability to exceed the latter. For the insurance company this implies

auditing the incoming claims with the highest probability possible as

well. For an illustration of the results obtained in Proposition 2(i) see

Figure 1(a) and the discussions in Section 4.1.

Proposition 2(ii) considers the policyholder point of view in this op-

timization problem. In this case, the decision whether to chose the fraud

probability as large or small as possible given a certain auditing strategy,

is not as clear as in the previous situation described in Proposition 2(i)

especially since there are situations for which no forecast can be made.

Furthermore, difficulties arise when trying to interpret the impact of sin-

gle model parameters on the value of the threshold that determines the

optimal auditing behavior in the known cases. However, see Figure 1(b)

and the discussions in Section 4.1 for an illustration of the optimal fraud


probability from the policyholder perspective.

The challenges that occur with finding a closed-form analytical so-

lution to the introduced maximization problem emphasize the need for

a numerical approach. In Section 3, we therefore present a method

for deriving the acceptance range for both policyholder and insurance

company. Furthermore, the impact of valid p − q combinations on the

objective quantities U(WA1 ) and NPV is analyzed and illustrated.

3 Computational Aspects

As discussed in the previous section, simple analytical solutions to the op-

timization problem cannot be derived for all general settings. Moreover,

the results may be hard to interpret both graphically and economically.

In this section, we will approach these challenges by using numerical

methods and Monte Carlo simulation. The aim is to compute the accep-

tance range with respect to the fraud and auditing strategies for various

parameterizations of the model. After having introduced the procedure,

the results of the simulations will be analyzed and presented graphically.

Monte Carlo Simulation and Numerical Methods

We use the Monte Carlo technique to find the optimal acceptance range

regarding the fraud and auditing strategies of the policyholder and the

insurance company respectively. The main idea behind this approach is

to generate a sufficiently large number of realizations N of the random

variable θ. Furthermore, we consider all fraud and auditing probabilities

p and q that are represented by l · 1M

for l = 0, 1, ...,M where M denotes

the number of discretization points on the interval [0, 1]. Based on these

assumptions, the resulting indemnity payments R, the policyholder’s

wealth positions with and without having signed the insurance contract

WA1 and WB

1 and the insurance company’s value V are calculated for

each outcome of the simulation and each fraud and auditing probability

combination. Using Equations (1), (6) and (8) for R, WB1 and WA

1

respectively, this can written as follows:


R[n, i, j] = (1 − p[i])θ[n] + p[i]((1 − q[j])αθ + q[j](θ[n] −B[n])) (18)

WB1 [n, i, j] = W0 − θ[n] (19)

WA1 [n, i, j] = W0 − Pθ[n] + R[n, i, j], (20)

where θ[n] denotes the nth realization of the random variable θ and p[i]

and q[j] are the considered fraud and auditing probability represented

by i 1M

and j 1M

for i, j = 0, 1, ...,M respectively. Consequently, the term

[n, i, j] indicates for which combination of loss realization and fraud and

auditing probabilities the quantities R, WB1 and WA

1 are evaluated.

The next step to determining the acceptance range is to derive the

objective quantities, i.e., the policyholder’s final utility depending on

whether he signed the insurance contract prior to the loss or not and the

insurance company’s present value based on the corresponding wealth

and value positions calculated before. For this purpose, we use arith-

metic averaging with respect to the realizations of the random variable

θ for each possible combination of p and q. Regarding the individual’s

final utility when having decided against insurance coverage, we use the

following formula, derived from Equation (10):

U(WB1 )[i, j] = µn(WB

1 [n, i, j]) −a

2σ2n(WB

1 [n, i, j]), (21)

where µn denotes the estimator for the expected value with respect

to all realizations n = 1, ..., N and σ2n the estimator for the variance with

respect to all realizations n = 1, ..., N . The same procedure applies for

the case when an insurance contract was signed, this time using Equation

(11):

U(WA1 )[i, j] = µn(WA

1 [n, i, j]) −a

2σ2n(WA

1 [n, i, j]). (22)

From the insurance company point of view, the net present value of

its future incoming and outgoing cash flows depending on the fraud and

auditing probability can be derived as follows, based on Equation (2):

NPV [i, j] = P − µn(R[n, i, j]) − q[j]k. (23)


We are now in the position to check for the participation constraints

of both the policyholder and the insurance company. Only if these hold

true, an insurance contract comes into existence and merely in this case,

the optimization problems are well defined. The idea here is to systemat-

ically analyze the participation constraints given in Equations (12) and

(3) for each combination of fraud and auditing probabilities. In case

these are verified, we consider the corresponding p − q combination as

valid. At the end of this procedure, we obtain the acceptance range.

The actual aim is to find the optimal strategies p and q such that the

objective quantities, i.e., the policyholder’s final wealth position U(WA1 )

and the present value of the insurance company’s future incoming and

outgoing cash flows NPV , are maximized from each of the participants’

perspectives. For these to be determined, we calculate the results for

U(WA1 ) and NPV evaluated with respect to the valid p − q combina-

tions respectively. Once the maximal values have been found, we can

retrace the corresponding fraud and auditing probabilities under which

the maximum was attained. This procedure is performed separately for

the two participants.

Choice of Parameters

We analyze the implementation of the model for different parameteriza-

tions. The aim here is to study the influence of certain model parameters

on the acceptance range regarding the valid fraud and auditing proba-

bilities.

We make assumptions concerning the distribution of the loss variable

θ, the policyholder’s initial wealth position W0 and the penalty payment

B that remain fixed throughout the whole analysis. For instance, the

policyholder’s wealth position is set to W0 = 0. Since his participation

constraint that is given by Equation (12) is independent of this param-

eter, our choice will not have any influence on whether he signs the

insurance contract or not. Furthermore, we assume the random variable

θ to follow a log-normal distribution. This assumption is commonly used


as mentioned in Marlin (1984) since it guarantees positive values for the

realizations of the random variable. In particular, the expected value is

set µ = 1 and the variance σ2 = 0.4. Regarding the penalty payment

B, we take it to be of the same value as the corresponding realization

of the loss θ such that in the case of detected fraudulent behavior the

indemnity payment is 0. Additionally, we will not consider exogenously

given penalties. Viaene and Dedene (2004) claim that in practice insur-

ance companies tend to negotiate with allegedly suspicious policyholders

since substantial legal evidence is needed to prosecute insurance claim

fraud successfully.

In this subsection, we analyze the influence of the policyholder’s risk

aversion a, the amount of fraud that is represented by α, the insurance

premium P and the cost per audit k on the acceptance range respec-

tively. For this purpose, we use the ceteris paribus assumption in the

analysis, i.e., we study the change in the acceptance range caused by

one isolated factor while keeping all the others constant. Unless noted

otherwise, the policyholder is taken to be risk averse. Hence, to start

with, his risk aversion parameter a is set 6. Furthermore, we first assume

that in the case of fraudulent behavior the policyholder always decides

to claim an amount that is 20% higher than the actual loss. According

to Derrig, Johnston, and Sprinkel (2006), this value seems reasonable.

In an auto injury insurance claim study from 2002, they revealed that

the average payments that were made related to bodily injury claims

added up to approximately $7,872 if no buildup or fraud was detected,

whereas in cases where fraudulent behavior appeared, the amount rose

up to $9,559 on average. The last assumption that we have to make con-

cerns the insurance premium. It can be split up into the fair premium

and an appropriate loading factor. The fair premium corresponds to the

expected loss. Hence, having set the expected value of the loss variable θ

to µ = 1, it implies a fair premium of 1 as well. However, the loss ratio in

the automobile insurance in many industrialized countries over the last

years averaged out to approximately 70%.4 Using this observation and

the assumption of µ = 1, we set the fair premium to 1.4. Furthermore,

since the insurance company faces additional costs due to the auditing

4See, e.g., U.S., German or Swiss market supervisory data.

4 Simulation Results 21

process with positive probability, it will add a corresponding loading fac-

tor to the fair premium. However, as mentioned in Cummins and Mahul

(2004), the loading factor cannot be chosen too big since potential poli-

cyholders would not sign the insurance contract under such conditions.

For the purpose of starting our analysis, we will assume the total insur-

ance premium to be P = 1.45. The last parameter whose influence on

the acceptance range will be analyzed is the cost per audit k. It is set

k = 0.1 which corresponds to 10% of the expected value of the loss θ.

For the purpose of our analysis and in order to keep focused, we will

disregard costs other than the ones due to auditing.

Table 1 sums up the choices for the input parameters for the reference

setting as introduced. In the course of this study, we base our simulations

and studies on these values.

Input parameter Reference level

Initial wealth position W0 0

Insurance premium P 1.45

Occurred loss θ lnN (1, 0.4)

Fraud amount α 1.2

Risk aversion parameter a 6

Auditing cost k 0.1

Penalty payment B realization of θ

Table 1: Input Parameters for the Reference Setting

Unless otherwise noted, the simulation results are based on N =

100, 000 realizations of the loss variable θ and M = 50 discretization

points in the interval [0, 1].

4 Simulation Results

This section contains the results based on the numerical simulation.

First, we discuss the reference setting and the impacts on the objec-

tive quantities and the corresponding optimal strategies. Furthermore,

a sensitivity analysis of the relevant parameters is performed.


4.1 Reference Setting

Before discussing the effects of different parameterizations regarding the

policyholder’s risk aversion, the amount of fraud, the insurance premium

and the cost per audit on the acceptance range, we will first illustrate

the results given the input parameters as summarized in Table 1.

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

(a) Insurance Company Perspective

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

(b) Policyholder Perspective

Figure 1: Acceptance Range from both Stakeholders’ PerspectivesAll parameters are chosen as presented in Table 1. p− q combinations which result in thehighest third of NPV and U(WA

1 ) respectively are displayed in the darkest color, the ones

which result in the lowest third of NPV and U(WA1 ) respectively in the lightest color and

the remaining ones in a medium color.

Figure 1 shows the acceptance range from both the policyholder and

the insurance company perspective based on the values for the input pa-

rameters that were presented above. Each point in the graphic represents

a valid fraud and auditing probability combination.

To illustrate the dimension of the objective quantities U(WA1 ) and

NPV that result from the current parameter choice and a certain p− q

combination, the points in Figure 1 are displayed in different colors ac-

cording to the value. For this purpose, given that the input parameters

are fixed, the p − q combinations that lead to the lowest third of out-

comes are presented in the lightest color, whereas those combinations

that result in the highest third of outcomes are shown in the darkest

color. The remaining points are displayed in a medium color. This im-

plies that the darker the color of a point, the higher is the relative value

4.1 Reference Setting 23

of the corresponding U(WA1 ) or NPV .

Insurance Company Perspective

From the insurance company point of view, we are interested in deriving

all feasible and, in particular, the optimal verification strategies charac-

terized by the probability of auditing q when the prevalent defrauding

probability p is known.

For this purpose, let some constant fraud behavior that is charac-

terized by p be given. The choice regarding the optimal corresponding

auditing strategy q from the insurance company perspective depends on

the value of the fraud probability p. As already proven in Proposition

2, there exists a threshold p∗ that determines whether it is optimal to

audit the incoming claims with the highest probability possible or the

lowest valid probability, i.e., the highest and lowest q respectively con-

tained in the acceptance range. Considering the choice of the input

parameters for the reference setting, the value of this threshold is given

by p∗ = k/αE(θ) = 0.083. This implies that in the case p > 0.083, it is

best for the insurance company to audit the incoming claims with the

highest valid probability whereas if p ≤ 0.083, the optimal strategy is

to chose q as small as possible. These relationships can be observed in

Figure 1(a).

Another interesting observation can be made when considering p = 1.

In this specific setting, the fraud-prone policyholders decide to inflate

their claims by 20% each time they incur an insured loss. Intuition would

tell us that such an extensive case of build-up cannot be acceptable from

the insurance company point of view, i.e., it would not be possible to

find feasible auditing strategies in this context. However, we are able

to observe the opposite in our analyses due to the circumstance that

the insurer in our reference setting has to incur relatively low costs to

detect fraudulent attempts. Additionally, in the case of proven build-up,

no indemnity payments are made to the policyholder, i.e., neither the

excess nor the loss amounts are paid out. As a consequence, it is possible

to have the savings from detected fraud outweigh the additional costs


from indemnifying inflated losses such that the net present value NPV

is positive. Thereby, the best result from the insurance company point

of view is achieved when performing audits with the highest feasible

probability q.

Policyholder Perspective

Similarly to the case above, we determine all acceptable and especially

optimal defrauding strategies p from the policyholder perspective, given

that they have knowledge of the current insurance company’s auditing

scheme q. The former are defined by the probability of filing an inflated

loss amount.

Hence, we assume the insurance company to be committed to some

constant auditing strategy q. From the policyholder perspective, it is

always optimal to correspond with reporting fraudulent claims at the

highest valid probability p. Figure 1(b) supports this result.

This finding appears to be rather intuitive. The premise in this con-

text is the insurance company having committed itself to some constant

verification scheme expressed by some constant probability q. However,

this implies that the share of incoming claims that does not have to

undergo the auditing process remains constant as well. In this case, it

is advisable for the policyholder population to increase the probability

p of exaggerating their loss amounts, i.e., the share of build-up among

the claims that are indemnified instantly rises as well leading to higher

payouts for the individuals.

As indicated in Section 1, Figure 1 illustrates that in the setting of our

model framework, it is impossible to find a feasible p−q combination that

maximizes the objective quantities of both stakeholders at the same time.

The prevalent behavioral strategies result in an optimum of either the

insurance company’s net present value NPV or the policyholder’s utility

U(WA1 ) of having signed an insurance contract prior to the occurrence of

loss. Which one of these events will be observed depends on the market

power of the respective parties. Assuming a highly competitive market,

it is likely for those defrauding and auditing probability combinations to

be applied that maximize the policyholders’ objective while the insurer

is still willing to adhere to the insurance relationship. However, if the

4.2 Sensitivity Analysis of Relevant Parameters 25

insurance company is in the position of possessing the position of power,

other probability combinations become of interest since the insurer will

be able to maximize its own objective while making sure to keep contract

conditions attractive enough for its policyholder population.

Furthermore, it seems possible for defrauding and auditing strategies

that have once been optimal for the respective stakeholder to become

unattractive in the consecutive observation period. Consequently, the

insurance company and the policyholders need to identify all acceptable

probability combinations p − q at the beginning of each period, and

possibly realign their strategies on this basis.

4.2 Sensitivity Analysis of Relevant Parameters

In the remainder of this section, we present and discuss the resulting

acceptance ranges, i.e., all valid p − q combinations based on different

choices regarding the input parameters of risk aversion a, fraud amount

α, insurance premium P and cost per audit k. Since the effects of the dif-

ferent valid p−q combinations on the policyholder’s final utility position

U(WA1 ) and on the insurance company’s present value NPV has been

presented and analyzed, we restrict ourselves to showing the acceptance

range itself without the impacts on the objective quantities.

Influence of Policyholder’s Risk Aversion

In this subsection, we will analyze the impact of different risk aversion

parameters on the acceptance range of the fraud and auditing probabil-

ities. For this purpose, we chose different values for a while keeping all

the other input parameters as given in Table 1. In particular, Figure 2

shows the acceptance range for the risk aversion parameters a = 5 and

a = 10.

Comparing the two graphics for the acceptance range, we find that

the upper bound shifts in an upward direction when increasing the pol-

icyholder’s risk aversion parameter. This implies that the higher the

risk aversion of the policyholder is, the broader the acceptance range

becomes assuming all the other input parameters to be constant.


0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g p

robability q

(a) Acceptance Range: a = 5

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g p

robability q

(b) Acceptance Range: a = 10

Figure 2: Acceptance Range for Different Risk Aversion Parameters aThe remaining parameters are chosen as presented in Table 1.

In other words, the more risk averse the policyholder is, the higher

the auditing probability q can be chosen for each fraud strategy p while

the policyholder is still willing to participate in the insurance contract.

Influence of Fraud Amount

In Figure 3, the acceptance range is displayed for the fraud amounts

α = 1.1 and α = 1.8 respectively, i.e., in the case of fraudulent behavior,

the claimed loss is given by θ = 1.1 ·θ or θ = 1.8 ·θ. Again, the remaining

input parameters are chosen as displayed in Table 1.

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

(a) Acceptance Range: α = 1.1

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

(b) Acceptance Range: α = 1.8

Figure 3: Acceptance Range for Different Fraud Amounts αThe remaining parameters are chosen as presented in Table 1.


Comparing the graphics for the different choices of α, we find that the

upper bound of the acceptance range as well as part of the lower bound

shift in an upward direction when increasing the fraud amount. To be

more precise: while the number of valid p − q combinations with high

auditing probabilities q increases for all fraud strategies p, the change

in the lower bound occurs only in the area of high fraud probabilities

p. Summing up these effects, we can state that the higher the amount

of fraud, the wider the acceptance range becomes. However, a change

from α = 1.2 in the reference setting to α = 1.1 results in marginal

modifications within the acceptance range.

This outcome can be interpreted in the following way: the higher the

amount of fraud α per claim, the more likely it is for the policyholder to

accept higher auditing probabilities q, given that his own fraud probabil-

ity p is fixed. In these cases, even though the auditing activity increased,

the gain in final utility U(WA1 ) due to excessive claiming is still posi-

tive, despite the higher chance of being convicted and imposed with a

penalty payment. On the other hand, it becomes unattractive from the

insurance company perspective to audit the incoming claims with a low

probability q when the amount of fraud is increased, assuming a high

fixed fraud behavior p. Such a strategy would imply that the majority

of fraudulent claims remained undetected, which consequently leads to

an increase in outgoing cash flows due to excessive fraud amounts. This

increase, however, is not covered by incoming positions like insurance

premiums or penalty payments. Therefore, if the fraud amount α goes

up, p − q combinations with higher values for q become acceptable to

both stakeholders, whereas no insurance contract will come into existence

with individuals who are expected to commit excessive fraud frequently.

Influence of Insurance Premium

Insurance premiums are another common way to influence the willing-

ness of both the potential policyholder and the insurance company to par-

ticipate in an insurance contract. In Figure 4, the acceptance range is pre-

sented for two different values of the insurance premium, i.e., P = 1.35

and P = 1.55 while the other input parameters are chosen as in the


reference setting.

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

(a) Acceptance Range: P = 1.35

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

(b) Acceptance Range: P = 1.55

Figure 4: Acceptance Range for Different Insurance Premiums PThe remaining parameters are chosen as presented in Table 1.

A comparison of the acceptance ranges when choosing P = 1.35 and

P = 1.55 respectively shows that the upper bound shifts in a downward

direction when increasing the value of the insurance premium. This

means that the higher the insurance premium is, the smaller the ac-

ceptance range gets while keeping the remaining input parameters un-

changed.

In other words, the lower the insurance premium P is, the more

willing the policyholder is to accept higher audit probabilities q when

keeping his own fraud probability p constant. However, if the insurance

premium is set too high, i.e., it exceeds the expected loss amount by

far, potential policyholders will have no benefit from signing such an

insurance contract.

The effect of shrinking acceptance ranges due to high insurance pre-

miums can be weakened by offering such contracts to potential policy-

holders whose risk aversion is assumed to be high as well. As we have

seen in Figure 2, the increase in risk aversion has the opposite effect on

the acceptance range as the choice of the insurance premium.

It needs to be pointed out that the insurance premium seems to have

a significant impact on the acceptance range. Even though the values of

P have been varied only marginally throughout the analysis, i.e., ≈ ±7%


of the reference level, the resulting number and positions of the valid p−q

combinations differ markedly.

Influence of Cost Per Audit

The last input parameter that can be adjusted easily is the cost per

audit k. Its value can give an indication of what type of auditing is be-

ing performed by the insurance company. Auditing procedures in which

standard techniques are applied require minor costs, whereas investiga-

tive processes that are initiated to verify major claims result in high

costs.

Figure 5 displays the acceptance ranges when the cost per audit is

chosen to be k = 0.01 and k = 1.0 respectively while keeping the remain-

ing input parameters as in the reference setting.

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

(a) Acceptance Range: k = 0.01

0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fraud probability p

Auditin

g pro

bab

ility q

(b) Acceptance Range: k = 1.0

Figure 5: Acceptance Range for Different Costs Per Audit kThe remaining parameters are chosen as presented in Table 1.

When comparing the graphic where the cost per audit is set k = 0.01

to the one with k = 1.0, we find that the upper boundary of the ac-

ceptance range shifts in a downward direction in the case of low fraud

probabilities p while there appears to be no change in the remaining

valid p−q combinations. This implies that the higher the cost per audit,

the smaller the acceptance range becomes when keeping the other input

parameters constant. However, only marginal changes within the accep-

tance range can be observed when choosing k = 0.01 instead of k = 0.1


as given in the reference setting.

This observation can be explained in the following way: the higher

the cost per auditing process, the less willing the insurance company

becomes to verify those incoming claims for which a low fraud probability

is assumed. Such a strategy would lead to high expenses for the insurer

that are not likely to be covered. The policyholder rarely commits fraud

and even in case he does, the additional amount claimed is not excessive.

Therefore, relatively high auditing costs and comparably low expenses

resulting from undetected fraudulent claims are opposing each other.

As a consequence, no insurance contracts will come into existence with

policyholders whose fraud probability p and amount α are expected to

be low while the cost per audit k is set at a high level.

A way to avoid this effect is to adjust the effort put into the auditing

process to each specific case. Depending on the type of loss and the cor-

responding amount claimed, the insurance company can decide whether

to apply a basic procedure at low cost or an extensive process that leads

to high expenses.

As indicated by the very extreme choice of the parameters, i.e., in

the first case k = 0.01 corresponds to 1% of the expected loss and in the

second one k = 1.0 equals the expected loss, the cost per audit k does

not have a significant influence on the acceptance range. However, the

results imply that extensive auditing in the form of high values for q is

not sustainable for the insurance company if the cost per audit k is high.

5 Conclusive Remarks

In this study, we build and analyze a model framework that depicts the

handling of insurance claims fraud based on a costly state verification

approach. We present analytical solutions as well as numerical methods

for solving the resulting optimization problems that take both the insur-

ance company and the policyholder perspectives into account. Our focus

is set on deriving an acceptance range consisting of all valid fraud and

auditing probability combinations and analyzing their optimality regard-

5 Conclusive Remarks 31

ing both stakeholders’ objective quantities respectively. In addition, we

discuss the impact of different relevant input parameters on the size of

the acceptance range. Furthermore, we are able to calculate a threshold

value for incoming claims based on which the insurance company can

decide whether to perform auditing or not.

One of our main findings is the derivation of optimal auditing and

fraud strategies from the stakeholders’ perspectives. Especially from

the insurance company point of view, it seems intuitive: the optimal

answer to low fraud probabilities is to perform auditing with a small

probability as well, whereas medium and high fraud probabilities require

the largest valid audit probability to maximize the net present value.

An interesting observation in this regard is that the insurance company

benefits from the existence of insurance contracts (almost) regardless of

the policyholders’ defrauding strategy. This finding demonstrates that in

the context of cost-minimizing insurers, it is not essential to completely

prevent all defrauding attempts ventured by the policyholder population.

Based on our numerical approach, we present and analyze the ac-

ceptance range for different parameterizations as well as the optimality

of different auditing and fraud probability combinations regarding the

stakeholders’ respective objective quantities. While a relatively high risk

aversion, a high relative amount of fraud and low insurance premiums

result in broadening the acceptance range, the latter becomes smaller

whenever the value of these input parameters is chosen the opposite way.

We also find that the cost per audit merely influences the number of

valid fraud and auditing probability combinations. Furthermore, the

simulation results support and illustrate our analytical findings regard-

ing optimal fraud and auditing strategies.

The model that we present in this study can be extended for future

research. On the one hand, another type of auditing could be introduced

that while less costly than the perfect one, detects fraud only with some

probability less than one. On the other hand, insurance premiums could

depend on the auditing probability since more strict auditing policies

require a longer period to process incoming claims and policyholders


might not be willing to pay the original insurance premium due to pos-

sible delays in indemnity payments. Another topic for further research

is to back test the results derived in this study with insurance company

data and profiling experience.

6 Appendix 33

6 Appendix

In the Appendix, we state the propositions and the corollary presented

in the main part of the paper once again and provide their proofs respec-

tively.

Proposition 1 For a = 0 and θ, θ such that 0 ≤ θ < θ, the optimal

fraud and auditing strategies from both stakeholders perspectives are

p = 1 and q = 0. This results in P = E(θ).

Proof of Proposition 1

By setting a = 0, the policyholder’s participation constraint given in

Equation (13) can be written as

P ≤ E(R(θ, θ)). (24)

Since both participation constraints have to be met for an insurance

contract to come into existence, (4) and (24) result in

E(R(θ, θ)) + qk ≤ P ≤ E(R(θ, θ)) ⇐⇒ q = 0 ∀k > 0, (25)

i.e., for any k > 0, q = 0 is the only solution.

In this case, the policyholder’s objective function (15) can be written

as U(WA1 ) = W0 − P + p[E(θ) − E(θ)]. Due to the assumption of θ < θ,

it attains its maximum at p = 1.

Furthermore, setting q = 0 and p = 1 in Equation (1), we get

E(R(θ, θ)) = E(θ). At the same time, one can conclude from (25) that

P = E(R(θ, θ)). This leads to P = E(θ). �

Proposition 2 Assume p, q to be in the acceptance range, i.e., an

insurance contract exists. For a > 0, B = θ, θ = αθ with some α ≥ 1,

the respective optimal strategies popt, qopt are given by:

(i) Insurance company perspective


Let some p be given. In order for the net present value NPV to

be maximized, choose

qopt =

{

as large as possible if p > p∗

as small as possible if p ≤ p∗, (26)

where p∗ := kαE(θ) .

(ii) Policyholder perspective

Let some q be given. In order for the final expected utility U(WA1 )

to be maximized, choose

popt =

as large as possible s.t. −E(θ)ap(1−α(1−q)) Var(θ) ≥ 1

as small as possible s.t. −E(θ)ap(1−α(1−q)) Var(θ) ≤ 0

. (27)

For 0 < −E(θ)ap(1−α(1−q)) Var(θ) < 1 no general statement can be made.

Proof of Proposition 2

(i) Using Equations (1), (2) and the assumptions B = θ, θ = αθ with

α ≥ 1, we get

NPV = P − (1 − p)E(θ) − p[(1 − q)E(θ) + qE(θ −B)] − qk

= P − (1 − p)E(θ) − p(1 − q)αE(θ) − qk

= P − E(θ) + p(1 − α)E(θ) + q[αpE(θ) − k]. (28)

Deriving (28) with respect to q leads to

∂

∂qNPV = αpE(θ) − k, (29)

which can be distinguished into two cases with respect to its sign.

6 Appendix 35

(a) If for the given fraud strategy p > kαE(θ) holds, the NPV as

defined in (2) has a positive slope with respect to the parame-

ter q. Consequently, the optimal auditing strategy qopt has to

be chosen as large as possible in order to maximize the value

of NPV .

(b) If the given fraud strategy p is given such that p ≤ kαE(θ) holds,

the NPV has a negative slope with respect to the parameter

q. Hence, the optimal auditing strategy qopt has to be chosen

as small as possible for the NPV to be maximized.

(ii) Applying the assumptions a 6= 0, B = θ, θ = αθ with α ≥ 1 to

Equations (1) and (11), we obtain

U(WA1 ) =W0 − P − E(θ) + (1 − p)E(θ) + p[(1 − q)E(θ) + qE(θ −B)]

−a

2Var[−θ + (1 − p)θ + p(1 − q)θ + pq(θ −B)]

=W0 − P − E(θ) + (1 − p)E(θ) + p(1 − q)E(θ)

−a

2Var[−θ + (1 − p)θ + p(1 − q)θ]

=W0 − P − pE(θ) + pαE(θ) − pqαE(θ)

−a

2Var(−pθ + pαθ − pqαθ)

=W0 − P − p(1 − α + qα)E(θ)

−a

2p2(1 − α + qα)2 Var(θ). (30)

Deriving (30) with respect to p results in

∂

∂pU(WA

1 ) = −(1 − α + qα)E(θ) − ap(1 − α + qα)2 Var(θ). (31)

Based on (31), three cases can be identified:

(a) For −E(θ)ap(1−α(1−q)) Var(θ) ≥ 1, the policyholder can choose any

fraud strategy p ∈ [0, 1], especially any p in the acceptance


range, such that p ≤ −E(θ)a(1−α(1−q)) Var(θ) . Applying this inequal-

ity to Equation (31), we obtain ∂∂p

U(WA1 ) ≥ 0. From this can

be concluded that U(WA1 ) has a positive slope. Consequently,

the optimal fraud strategy popt has to be chosen as large as

possible in order to maximize the value of U(WA1 ).

(b) Similarly, for −E(θ)ap(1−α(1−q)) Var(θ) ≤ 0, the policyholder can

choose any fraud strategy p ∈ [0, 1], especially any p in the

acceptance range, such that p ≥ −E(θ)a(1−α(1−q)) Var(θ) . For Equa-

tion (31) this implies that ∂∂p

U(WA1 ) ≤ 0. This means that in

this case U(WA1 ) has a negative slope and hence, the optimal

fraud strategy popt needs to be chosen as small as possible for

U(WA1 ) to be maximized.

(c) For 0 < −E(θ)a(1−α(1−q)) Var(θ) < 1, no general statement about

the corresponding optimal fraud strategy popt can be made.

�

References 37

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Redistribution, Quarterly Journal of Economics, 104(2):399–415.

Moreno, I., F. Vazquez, and R. Watt, 2006, Can Bonus-Malus Alleviate

Insurance Fraud?, Journal of Risk and Insurance, 73(1):123–151.

Picard, P., 2009, Costly Risk Verification without Commitment in

Competitive Insurance Markets, Games and Economic Behavior,

66(2):893–919.

Picard, P. and M.-C. Fagart, 1999, Optimal Insurance Under Random

Auditing, Geneva Papers on Risk and Insurance Theory, 24(1):29–54.

Tennyson, S., 2008, Moral, Social, and Economic Dimensions of Insur-

ance Claims Fraud, Social Research, 74(4):1181–1204.

Townsend, R., 1979, Optimal Contracts and Competitive Markets with

Costly State Verification, Journal of Economic Theory, 21(2):265–293.

Viaene, S. and G. Dedene, 2004, Insurance Fraud: Issues and Challenges,

Geneva Papers on Risk and Insurance - Issues and Practice, 29(2):313–

333.

References 39

Watt, R., 2003, Curtailing Ex-Post Fraud in Risk Sharing Arrangements,

European Journal of Law and Economics, 16(2):247–263.

Weisberg, H. and R. Derrig, 1991, Fraud and Automobile Insurance: A

Report on Bodily Injury Liability Claims in Massachusetts, Journal

of Insurance Regulation, 9(4):497–541.

41

Part II

The Impact of Auditing

Strategies on Insurers’

Profitability

Abstract

Insurance claims fraud is a major concern in the insurance industry. Ac-

cording to estimates, excess payments due to fraudulent claims account

for somewhere between 15 and 25 percent of all claim payments, affect-

ing all classes of insurance. In this paper, we develop a model framework

based on a costly state verification setting in which - while policyholders

observe the amount of loss privately - the insurance company can decide

to audit incoming claims at some cost. The aim is to derive optimal

auditing strategies from the insurance company perspective while main-

taining contract attractiveness to policyholders who are willing to adhere

to the insurance relationship. We present and analyze an auditing strat-

egy which is triggered by the filed claims amount and also includes an

option for each stakeholder to adapt its behavior based on a signal spe-

cific to its position. The impact of the optimal auditing strategy on the

insurer’s profitability is examined. Finally, practical implementations

are discussed. 5

5K. Muller, H. Schmeiser, and J. Wagner. The Impact of Auditing Strategies onInsurers’ Profitability. Working Papers on Risk Management and Insurance, 2012.This paper has been presented at the International Congress on Insurance: Math-ematics and Economics in June 2012, the European Group of Risk and InsuranceEconomists Seminar in September 2012 and the Annual Meeting of the Western Riskand Insurance Association in January 2013.It is currently in the second round of the review process at The Journal of Risk and

Insurance and has been resubmitted in November 2012.

42 II Theory of Insurance Fraud

1 Introduction

Insurance claims fraud is one of the major industry concerns. It occurs

in all classes of insurance and accounts for a substantial portion of the

indemnity payments each year, yet due its nature, is difficult to estimate

in total value. The Insurance Research Council (2008) estimated the

excess payments due to fraudulent claims in 2007 as somewhere between

$4.8 and $6.8 Mrd in the auto injury insurance sector in the U.S. alone,

corresponding to 13 to 18 percent of total payments. These fraudulent

activities, while undertaken by some individuals, have an impact on the

policyholder population as a whole through higher insurance premiums

(see Tennyson (2008)).

Previous research has explained the existence of fraud due to infor-

mation being asymmetrically distributed between policyholder and the

corresponding insurance company (see, e.g., Derrig (2002)). Since in-

sureds may hold private information about the actual amount of the

loss suffered, there exists the possibility of misrepresentation. Based

on the approach of costly state verification (see, e.g., Townsend (1979),

Mookherjee and Png (1989), Bond and Crocker (1997), Picard and Fa-

gart (1999), Picard (2000)), the insurance company can consequently

choose to audit incoming claims in order to determine their truthful-

ness. In cases when fraudulent activities haven been proven, a penalty

payment can be imposed on the policyholder. However, these verifica-

tion processes incur costs. From the insurance company perspective this

implies that the costs for auditing have to be traded off against the

savings resulting from detected fraud. One of the costs may be on poli-

cyholder attitude, and therefore additionally, the policyholders’ point of

view needs to be considered as well. According to Viaene and Dedene

(2004), individuals are more likely to develop an opportunistic attitude

towards insurance fraud after having gained negative experiences with

their insurance companies. Underpaid claims or the endurance of long

waiting periods for indemnity payments may encourage fraudulent be-

havior in the future.

1 Introduction 43

An opposing strategy to minimize the occurrence of insurance fraud

comprises the implementation of bonus-malus systems. Dionne and

Vanasse (1992) and Moreno, Vazquez, and Watt (2006) develop model

frameworks where, instead of performing costly verification processes,

the policyholder’s insurance premium is increased whenever he or she

files a claim in the previous period. This approach is applicable in the

case of insurance contract renewals; however, in some countries policy-

holders may avoid this penalization mechanism by switching their insur-

ance company (see, e.g., Dionne and Ghali (2005)).

An additional strand of research dealing with the occurrence and

handling of insurance claims fraud is based on the costly state falsifica-

tion approach introduced by Lacker and Weinberg (1989) and adapted

to the insurance setting by Crocker and Morgan (1998) and Crocker and

Tennyson (2002). While the premise with regard to the asymmetric dis-

tribution of information remains unchanged, this time the policyholder

engages in costly manipulations such that a verification of the claims

becomes impossible.

The term fraud has a rather negative connotation implying the en-

gagement in illegal activities such as staged accidents. The range of

actions, however, which is colloquially subsumed under this notion, is by

far broader (see, e.g., Picard (2001), Derrig (2002), Tennyson (2008)). In

general, a distinction is made between ex-ante and ex-post moral hazard,

referring to the timing of fraudulent behavior. The former occurs by the

time of insurance purchase, e.g., in case the potential policyholder fails

to provide relevant information which might have resulted in unfavorable

contract conditions or even in a rejection on part of the insurance com-

pany (see, e.g., Picard (2001)). The term ex-post moral hazard implies

the engagement in fraudulent activities by the time of claims filing, i.e.,

after a potential loss has been suffered. In this context, there are sev-

eral possible distinctions which can be made. A common one is to differ

between criminal fraud, also called hard fraud, and soft fraud which is sit-

uated in an ethical gray area (see, e.g., Tennyson (2008)). Derrig (2002)

defines criminal fraud as ”the willful act of obtaining money or value

from an insurer under false pretenses or material misrepresentations”.


While it is assumed that only a small number of claims contain outright

fraud, the more frequent and more costly type of fraudulent behavior

falls within the term of soft fraud (see, e.g., Weisberg and Derrig (1991),

Viaene and Dedene (2004), Tennyson (2008)). Even though there does

not exist an explicit definition of the term, it is associated with the mis-

representation of the loss magnitude after its occurrence, i.e., claimants

exaggerate the amount to obtain higher indemnity payments. A notion

often used in this context is build-up. In this paper, we will refer to

fraud as soft fraud or build-up, i.e., we assume that some policyholders

inflate the magnitude of loss after its occurrence if it appears profitable.

In addition to the policyholders, also third parties like service provid-

ers might be involved in fraudulent activities to exaggerate the loss

amount (see, e.g., Tennyson (2008), Dulleck and Kerschbamer (2006)

Derrig and Zicko (2002)). Prominent examples are known from auto-

mobile insurance. Derrig and Zicko (2002) found that repair shop are

likely to have developed insight about the insurance companies’ preva-

lent auditing strategies due to repeated experiences in repairing cars for

insured damages. As a consequence, there exists the possibility to adjust

the defrauding strategy. Such actions are either undertaken without the

knowledge of the policyholder, or performed by mutual agreement be-

tween the policyholder and the corresponding repair shop. The service

providers’ incentive to engage in fraudulent activities against the insur-

ance company may stem from the hope to gain the policyholders’ favor.

As a result, the latter might request their services again at a later point

in time. For the purpose of our study, we will assume that all fraudulent

activities - even if committed by repair shops - to be advantageous for

the policyholders only.

Considering its large prevalence, effective measures in dealing with

the phenomenon of insurance claims fraud need to be found. As already

mentioned, insurance companies have the possibility to perform audits.

Many insurers have dedicated teams to identify and combat fraudulent

claims. In interviews with fraud managers, Morley, Ball, and Ormerod

(2006) find that verification processes are initiated whenever investiga-

tors detect anomalies or inconsistencies in the circumstances of the loss

1 Introduction 45

event or unusual behavior from the claimant. This approach seems to be

suitable for filed claims that exhibit obvious signs indicating potential

fraudulent behavior and/or the ones which are of significant magnitude.

Apparently, high-magnitude claims are be subject to verification right

away. The majority of claims, however, appear to be legitimate at first

sight, seeking low to medium indemnity payments, which do not trigger

immediate investigation. Consequently, the key question is how to deal

with the fraudulent cases that appear legitimate, and which account for

the majority of inappropriate indemnity (see, e.g., Derrig (2002)).

We therefore set our focus on developing audit strategies which help

to improve the efficiency of the claims settlement process with regard to

inconspicuous claims. The key element in our model framework - which

pursues the costly state verification approach - is the use of threshold

values which indicate whether an incoming claim should be verified or

not. This approach allows the insurer to determine the optimal auditing

strategy based on the magnitude of the filed claim. For this purpose,

we make use of information on policyholder claiming and, more impor-

tantly, defrauding behavior which insurance companies are expected to

hold due to previous experiences and verification processes. In partic-

ular, the share of fraud-prone policyholders among the population has

an impact on the actual threshold values for auditing. Interviews with

experts as well as previous research (see, e.g., Belhadji, Dionne, and

Tarkhani (2000), Bermudez, Perez, Ayuso, Gomez, and Vazquez (2008))

have shown that numerous criteria exist which help indicate the poten-

tial fraud behavior of an individual. Such factors may include gender,

nationality or place of residence. Additionally, investigations in the past

have shown that certain accidents are more prone to fraud than others.

For example, wind screen and glass damages as well as thefts inside the

passenger compartment are known to be cases where policyholders are

likely to report exaggerated claim amounts. Combining this information

on individual characteristics with fraud signals presented by Dionne, Giu-

liano, and Picard (2009)), one obtains accurate estimators for the share

of defrauders among the claimants.


In what follows, a model framework is presented based on a costly

state verification setting in which - while policyholders observe the amount

of loss privately - the insurance company can decide to audit incoming

claims at some cost. Our goal is to derive optimal auditing strategies

from the insurance company perspective indicating which of the incom-

ing claims are subject to verification. In any case, we take into account

that contract conditions must still be attractive to policyholders such

that they are willing to adhere to the insurance relationship. A key

element of our study is the option of both stakeholders adapting their

behavior respectively based on different signals is taken into account.

Subsequently, the impact of the optimal auditing strategy on the insur-

ers’ profitability is analyzed.

Unlike other strands of research in this area (e.g., Townsend (1979),

Picard and Fagart (1999)), which often set up the problem of optimizing

insurance contracts in a way such that policyholders always report loss

amounts truthfully in equilibrium, we do not develop an auditing scheme

which completely prevents or deters insurance claims fraud. From a

macroeconomic point of view, both the approach and the result are

desirable. From a single company perspective, however, this does not

necessarily hold true. Similarly as Dionne, Giuliano, and Picard (2009),

our aim is to minimize the insurer’s overall costs from fraud, in general

including paying some portion of fraudulent claims, as well as incurring

expenses to detect and address fraud, and in experiencing the reputa-

tional effects of investigations themselves. In fact, we can show that for

low costs per audit process the insurance company’s net present value

increases in the presence of fraud compared to the case where no fraud

exists. Our findings are in line with the assumption made by Watt

(2003).

Allowing for the existence of some fraudulent activities accounts for

the widespread attitude to consider insurance as an investment which

is expected to yield a return. As evidence, a study from GDV (2011)

reported that more than 20% of the Germans consider insurance fraud

to be a ”gentlemen’s offence” which is committed by almost everyone at

least once. This point of view can be found among all socio-demographic

1 Introduction 47

groups. Duffield and Grabosky (2001) compile different approaches indi-

viduals use to justify fraud. Among others, insurance fraud is assumed

to cause no significant harm; insurers are accepted targets which can

afford it; build-up is a way to recover past premium payments (see also

Miyazaki (2008)). Given this line of reasoning, we assume therefore that

there will always exist policyholders trying to defraud in terms of inflat-

ing their magnitude of loss. In this context, auditing processes can help

to minimize the share of fraudulent activities among the policyholder

population. But a complete eradication seems unlikely.

Including the option to change one’s strategy based on signals pro-

vides another insightful result. We can show that there exist situations

where - while the possibility to adapt one’s behavior might be desir-

able for the insurance company - this option is disadvantageous from

the policyholder perspective. This observation stands in contrast to the

widespread opinion that the adaptation of the defrauding strategy, espe-

cially based on signals from service providers, would be favorable from

the individuals point of view.

We assume that while the policyholders and the service providers,

which might be involved, may obtain signals and information based on

which they change the defrauding strategy, they do not know the exact

auditing threshold values nor do they have enough information to derive

them themselves. This is a crucial assumption in our model which also

seems to be realistic. Leaving out this assumption, any auditing strategy

would be redundant since the policyholder would know how to adapt his

fraud behavior in a way to avoid being caught. From the insurance com-

pany perspective, it would not make sense to verify any incoming claim

in this case.

The remainder of this paper is organized as follows: We start by

presenting the model framework and optimization problem in Section 2.

Section 3 constitutes the introduction of the policyholder’s and insurer’s

respective strategies as well as the behavioral adaptation process. The

corresponding numerical results are presented in Section 4. In Section 5,

we analyze practical implications, before we conclude in Section 6.


2 Model Framework and Stakeholders’

Positions

We consider an insurance company with a fixed number of policyholders.

The latter are assumed to differ from one another only in their willingness

to defraud, i.e., the population consists of both honest individuals who

never commit fraud and those who defraud if it appears to be profitable.

We denote the share of fraud-prone policyholders among the population

with p. Depending on the loss amount and the prevalent defrauding

strategy, the share of claims which actually contain build-up might be

lower.

Since we assume all individuals to belong to the existing policyholder

population, they all pay an insurance premium P at the beginning of a

period, i.e., in t = t0. We assume this premium to equal the given market

premium which is demanded by other existing insurance companies as

well. At the same time, with probability 0 ≤ π ≤ 1, they face some

uncertain loss θ of stochastic amount which, by the time of occurrence,

is observed privately. In case a policyholder suffers a loss, he chooses

to file a claim of some size Θ(θ) during the period (t0, t1). In case of

honest behavior, the amount of the claim will equal the actual loss, i.e.,

θ = θ. If the individual decides to defraud, he reports some finite θ > θ.

Equation (32) summarizes all values the policyholder can report to the

insurance company in the claiming scheme Θ:

θ = Θ(θ)

= 0, no loss occurred

= θ, loss but no fraud

> θ, loss and fraud

. (32)

In the course of this paper, we will use the notation

F = {θ|θ > θ} (33)

to denote the set consisting of all fraudulent claims filed by the policy-

holders. The elements in F are characterized by the individuals’ defraud-

ing strategy. We will analyze different scenarios for the fraud behavior

in the course of this paper.

2 Model Framework and Stakeholders’ Positions 49

The insurance company however has no information about the true

loss amount. It therefore has the opportunity to verify the truthfulness

of incoming claims. However, this comes at some cost per audit k. In

this model framework, we take the audit process to be perfect, i.e., fraud

is detected with probability of one anytime auditing is performed. As

a consequence of detected fraud, the insurance company will reject any

indemnification.6 Figure 6 illustrates the interaction of the different

processes introduced in this model framework.

Following Figure 6, the payment of an indemnification depends on

several aspects. On the one hand, the policyholder needs to have suffered

an insured loss7 during the course of the observation period. Otherwise,

he would not have a reason to file a claim. In the case when the claimant

decides to defraud, his indemnification is dependent on whether auditing

takes place or not: If the reported loss is not verified, he receives the

payment of θ. If the filed claim undergoes an auditing process, however,

the attempt to defraud will be revealed and any indemnification payment

will be rejected, i.e., both excess and actual loss amount are denied. In

case the policyholder belongs to the group of honest individuals, his loss

θ will be indemnified no matter whether auditing took place or not.

Two key elements in the model framework which we have not elabo-

rated on so far, are the behavioral strategies of both stakeholders: The

amount of the reported claim in case of dishonesty is defined by the

policyholders’ defrauding behavior, while the decision whether or not to

induce a verification process is dependent on the insurance company’s

auditing strategy. We present and analyze different examples for the

respective strategies as well as behavioral adaptations in Sections 3 and

4.

6In practice, gradations with regard to the indemnification are possible, i.e., theinsurer might decide to pay the full loss amount or parts of it.

7Remember that we are considering only the situation where fraud will be com-mitted through claim build-up and not through planned fraud.

50IITheoryofInsuranceFraud

Policyholder

Claims Filing

Insurance Company

Claims Processing

No

Claim

θ

Original

Claim

θ ≥ θ

Claim

Submitted

Audit

?

No Audit

Verification

at cost k

Resu

lt

No Fraud θ = θ

Fraud θ > θ

Claiming depends on

policyholders’ behavior

Selection of claims for auditing

depends on insurer’s strategy

(No)

Indem

nification

Premium

Payment

Figure 6: Overview of the Processes Associated with the Filing and Handling of Insurance Claims over theCourse of One PeriodAn indemnification may or may not be paid out by the end of the period depending on the previous events.


Insurance Company: Contribution Margin and


From the insurance company perspective, we observe the future cash

flows at the beginning of a period in t = t0 and at the time of loss

realization and settling at the end of that period in t = t1 and analyze the

resulting contribution margin per contract CM in (t0, t1). The insurance

company receives a premium payment P from each policyholder in t =

t0. As already presented in the beginning of Section 2, the outflows of

each period in t = t1 depend on whether claims have been filed by the

policyholders, and if so, whether they were audited or not and the result

of the eventual verification process (see Figure 6).

A key element in this model framework is the insurance company’s

auditing strategy. It indicates which of the incoming claims are subject

to verification and which of them are indemnified without verification.

We use the following general notation to denote the auditing strategy

A = {θ|θ is audited}. (34)

We distinguish four scenarios which lead to different values in the

contribution margin for a single contract CM(P, k, θ,A,F). Using the

notations introduced in Equations (33) and (34), we define

CM(P, k, θ,A,F) =

P , no loss occurred, i.e., θ = 0

P − θ , no audit, i.e., θ ∈ Ac

P − θ − k , audit, no fraud, i.e., θ ∈ A ∩ Fc

P − k , audit, fraud, i.e., θ ∈ A ∩ F

, (35)

which can also be the stated as:

CM(P, k, θ,A,F) = P − θ · 1Ac(θ) − θ · 1A∩Fc(θ) − k · 1A(θ)

= P − θ[

1 − 1A∩F (θ)]

− k · 1A(θ), (36)


where 1X(y) denotes the indicator function, i.e., it takes the value 1 if

y is in the set X or 0 if y is not in X.

Hence, in this context 1A(θ) represents the number of claims which

were subject to verification whereas 1Ac(θ) states the number of claims

which were indemnified without auditing. 1A∩F (θ) counts the number

of cases when fraudulent claims underwent an auditing process, i.e.,

the number of cases when the attempt to defraud was unveiled while

1A∩Fc(θ) returns the number of cases when honest claims where verified.

Overall, the insurance company is interested in its whole policyholder

population and hence considers the average contribution margin per con-

tract E(CM), i.e., the net present value of future incoming and outgoing

cash flows NPV . We define :

NPV = NPV (P, k, θ,A,F) = E(CM(P, k, θ,A,F)), (37)

where E(Y ) denotes the expected value of the stochastic variable Y .

Hence, we analyze the insurance company’s net present value as the ex-

pected value of future cash flows discounted at the risk-free rate rf = 0.

This assumption rf = 0 holds throughout the paper.

Based on Equation (2), we can formulate the insurance company’s

participation constraint.

Condition 3 The insurance company is willing to maintain the insur-

ance relationship with its policyholder population if the net present value

per contract is non-negative:

NPV ≥ 0. (38)

Policyholder: Expected Utility and Participation

Constraint

From the policyholder perspective, we analyze their wealth positions

and the corresponding average expected utility at the end of the period

t = t1 in the framework introduced above. We assume each individual


initially to hold the same wealth position W 8 and to take out the same

insurance contract. At the beginning of the observation period in t = t0,

the payment of the insurance premium P is due. Consequently, each

policyholder is endowed with the wealth position W I0 = W − P , where

the superscript I indicates the existence of an insurance contract.

The consecutive development of this wealth position W I0 depends on

whether the policyholders suffer an insured loss and if so, whether they

choose to report their loss truthfully or not and whether their fraud is

being revealed in case of dishonesty or not. Taking the occurrence of loss

into account, the wealth position at the end of the observation period in

t = t1 is given by

W I1 = W − P − θ + θ

[

1 − 1A∩F (θ)]

, (39)

where W is invested riskless with rf = 0. In the case when no insured loss

has occurred throughout the observation period, Equation (39) simplifies

to W I1 = W I

0 = W − P .

In order to be able to formulate a participation constraint from the

policyholder perspective, we consider the development of their wealth

position throughout the observation period when not having signed an

insurance contract prior to the occurrence of loss. In t = t0, the indi-

viduals would not have to make a payment in the amount of the insur-

ance premium. Hence, the corresponding wealth position is given by

WN0 = W , where the superscript N implies the absence of an insurance

relationship. If some loss θ occurs up until t = t1, this amount decreases

to WN1 = WN

0 −θ = W−θ, whereas, without loss during the observation

period, we have WN1 = WN

0 = W .

We assume the policyholders’ expected utility to be described by

a standard mean-variance utility function of the corresponding wealth

position. The degree of risk aversion is expressed by the parameter

8Since the actual value of the initial wealth position will have no impact on thedecision whether to maintain the insurance relationship or not, the policyholdersmight even be endowed with different wealth positions. We assume the latter to beinvested safely with the risk-free rate rf = 0.


a (> 0). Generally, for a given stochastic wealth position Z, its expected

utility for the individual is given by U(Z) = E(Z) − a2Var(Z), where

Var(Z) denotes the variance of the stochastic variable Z.

Using the equations above and considering that the probability of

loss occurrence is denoted by π, the final expected utility in case no

insurance contract exists can be written as

U(WN1 ) = W − πE(θ) −

a

2π2Var(θ). (40)

Similarly, for the setting where an insurance relationship between

policyholders and insurance company already exists, the final expected

utility is given by

U(W I1 ) = W − P − E

(

πθ − θ[

1 − 1A∩F (θ)])

−a

2Var

(

πθ − θ[

1 − 1A∩F (θ)])

. (41)

Comparing Equation (41) with Equation (40) results in the policy-

holders’ participation constraint. For this purpose, we introduce the

notion of the gain in expected utility from having signed an insurance

contract

∆U = U(W I1 ) − U(WN

1 ). (42)

Condition 4 The policyholders are willing to maintain the insurance

relationship with the insurance company if their final expected utility is

greater with having insurance than without it, i.e.,

∆U ≥ 0. (43)

We want to point out that the policyholders’ participation constraint

functions the same in the case of a multi-period model, i.e., they do not

quit the insurance relationship unless their gain in expected utility from

having insurance coverage ∆U is negative. In particular, the insurance

company is in the position to optimize its position while the policyholders

would choose to cancel their insurance contracts only if ∆U < 0.

2.1 Optimization Problem 55

2.1 Optimization Problem

Summing up the information we have presented so far with regard to

the model framework as well as the insurance company’s and the poli-

cyholders’ participation constraints, we can formulate the resulting op-

timization problem.

The insurance company is aiming to derive an auditing strategy A

such that its net present value of future cash flows NPV is maximized.

At the same time, it needs to be made sure that the stakeholders are

willing to maintain their insurance relationships, i.e., Equations (38) and

(43) hold. Formally, this objective is given by

maxA

NPV (P, k, θ,F ,A)

NPV ≥ 0

∆U ≥ 0

. (44)

We make the assumption that the former charges the given market

premium P . In particular, this implies that an adaptation of the insur-

ance premium as part of the fraud handling is not feasible. Furthermore,

we assume no interaction with the number of acquired contracts.

3 Optimal Auditing Strategies

Section 2 constitutes the introduction of the model framework as well

as the insurance company’s and policyholders’ behavioral strategies in

general. In this section, we present a case for the individuals’ defrauding

behavior as well as a suitable approach to deriving the resulting optimal

auditing strategy. Furthermore, the process of behavioral adaptation is

included.

3.1 Policyholder Claiming Scheme

As discussed above, we consider insurance fraud in the form of build-up,

i.e., in the case of occurrence of loss some of the policyholders among the


population decide to file an exaggerated fraudulent claim if it appears

to be profitable.

In the context of our study, we assume that the fraud amount by

inflating the magnitude of a loss not be a decision variable for the policy-

holders. In case an individual decides to engage in fraudulent activities,

he or she will consider the build-up as a percental ”surcharge” on the ac-

tual loss amount instead of filing some value which deviates significantly

from the actual loss amount. This approach increases the likelihood of a

fraudulent claim to be perceived as legitimate by the insurance company,

and not to be audited as a consequence. This assumption is in line with

Viaene and Dedene (2004) who find that policyholders involved in soft

fraud typically tend to file claims containing small fraud amounts. Fur-

ther evidence can be found in the behavioral economic theory literature.

Individuals weigh the consequences accompanied by losses stronger than

the ones from a gain of the same size (see, e.g., Kahneman and Tversky

(1979), Kerr (2012)). Applied to the context of our model framework this

implies that the loss from being caught committing soft fraud (i.e., in-

demnification is waived completely) is perceived as a higher burden than

the potential profit from a successful build-up attempt. Additionally, re-

garding build-up as a surcharge on the loss suffered gives policyholders

the opportunity to ”back down and claim the appropriate amount” if in-

vestigated by the insurance company rather than in the case of outright

fraud (see, e.g., Emerson (1992)).

From the perspective of the repair shops, which might also be in-

volved in fraudulent activities, extensive inflations of the loss amount

seem to be unlikely as well. According to Hubbard (2002), service

providers in general have a reputational incentive to act in their clients

favor since the latter tend to return more often if they are satisfied with

previous services. These findings are in line with statements made by

experts from an insurance company whose experiences have shown that

repair shops orientate themselves on the actual loss amount when try-

ing to charge too much for certain services. This way even exaggerated

claims seem legitimate and are less likely to undergo an auditing process

resulting in direct indemnification.

3.1 Policyholder Claiming Scheme 57

As part of the defrauding strategy, we assume that whenever those

policyholders have suffered a loss during the observation period, they

report back a multiple of the actual loss amount. We denote this con-

stant multiplicative factor by α = θ/θ. However, it is well known that

insurance companies do perform audits in order to verify the truthful-

ness of incoming claims. Consequently, fraud-prone policyholders can

be expected to adjust their fraud strategy accordingly. We assume that

all of these individuals have an inner threshold value for defrauding θ∗ph.

With regard to their fraud strategy this threshold value implies that they

apply their fraud strategy α up to the preset threshold value θ∗ph. To

be more precise, if the amount of the actual loss θ is smaller than the

threshold θ∗ph, the minimum of αθ and θ∗ph is reported to the insurance

company. However, if the amount of the loss suffered already exceeds

that threshold, the policyholder claims this amount truthfully. We can

write this strategy as

θ = Θ(θ, α, θ∗ph) =

0 , no loss occurred

θ , no fraud or θ > θ∗ph

min{αθ, θ∗ph} , fraud and θ < θ∗ph

. (45)

The set consisting of all fraudulent claims associated with this strat-

egy Θ(θ, α, θ∗ph) is denoted by Fα,θ∗

ph.

The question arises as to how policyholders determine an adequate

threshold value for defrauding. Here we refer to the data presented in

Section 1 regarding survey reports indicating that policyholders may

use third parties, such as repair shops, to act as their partners in fraud.

These repair shops are likely to have developed insight about the value

of θ∗ due to repeated experiences in repairing cars for insured damages.

Based on this information they can make proper assumptions concerning

the insurance companies’ prevalent auditing strategies. There are two

potential ways repair shops can proceed: provide too much service or bill

too much for a particular service (see Dulleck and Kerschbamer (2006)).

A particular phenomenon is to include the cost to fix existing damages


when repairing the ones which were caused by a current insured event.

Such actions might often be undertaken even without the knowledge of

the policyholder. On the one hand, the latter might not have the in-

centive to carefully check the work performed by repair shops since the

bill is passed on to the insurance company (see Tennyson (2008)). On

the other hand, the policyholders might lack the necessary know-how to

do so (see Dulleck and Kerschbamer (2006)). Policyholders, however, in

particular the ones who are willing to defraud if it appears to be advan-

tageous, may also seek information themselves to adapt their claiming

behavior for purposes of defrauding the insurer. They may seek out

others for ideas of successful fraud or perhaps be approached by third

parties to participate in defrauding activities. Staying in the field of

auto insurance, fraudulent activities may be performed by mutual agree-

ment between the policyholder and the corresponding repair shop who

share the excess insured payments with one another. In particular, there

exists the possibility to adjust the policyholders’ defrauding strategy as

presented in Equation (45). Recall that we make the crucial assumption

that neither the policyholders nor a third party other than the insurance

company itself holds exact information concerning the prevalent audit-

ing strategy. The contrary case would make the principal of auditing

redundant.

3.2 Insurance Company Auditing Strategy

From the insurance company perspective, this fraud strategy implies

the necessity to adjust its auditing strategy A. After having performed

audits for at least one period, the company should have gained enough

information on policyholder fraud behavior to do so. Revealed fraud

can serve as an especially helpful information base for improving the

existing auditing strategy. Assuming that a sufficiently high number of

verification processes has been performed (which has revealed sufficiently

many defrauding attempts), the insurer will note that fraudulent claims

do not exceed a certain threshold value. Hence, it is unnecessary to

audit claims above that value, allowing insurers instead to verify medium

sized claims. Consequently, in this case the aim is to derive the optimal

3.2 Insurance Company Auditing Strategy 59

auditing range AR. The upper bound of this range would have to be

the policyholders’ persistent inner threshold value θ∗ph. Unfortunately,

the insurance company does not hold this information. However, an

adequate estimate for this value is the maximum fraud amount which

was detected during the last period. We denote this value by θmax and

formally define it as

θmax = max{θ · 1A∩F}. (46)

Setting the upper bound of the auditing range AR to θmax practically

implies that no incoming claim above that value will be verified. How-

ever, since one cannot be absolutely sure whether the actual maximum

of all fraudulent claims has been determined, i.e., whether or not fraud is

being committed beyond θmax, it is reasonable to include a safety margin

s > 0. Consequently, the updated upper bound of the auditing range is

set (1 + s) · θmax.

The second parameter that characterizes the audit range AR is its

lower bound which is expressed by θ∗R. Summing up, we can formulate

this auditing strategy as

AR = AR(θ∗R, s, θmax) = {θ|θ∗R ≤ θ ≤ (1 + s) · θmax}. (47)

We can specify the optimization problem given in Equation (44) with

regard to this new setting. The aim here is to derive the optimal lower

bound θ∗R of the auditing range such that the insurance company’s net

present value NPV is maximized:

maxθ∗

R

NPV (P, k, θ,Fα,θ∗

ph,AR)

NPV ≥ 0

∆U ≥ 0.

(48)

As already mentioned above, the auditing strategy AR requires the

availability of information with regard to the prevalent defrauding behav-

ior, i.e., θmax needs to be determined. Consequently, AR is applicable

after the first observation period the earliest when enough audits have


been performed to specify the value of θmax. However, this implies the

need for a different verification scheme for the very first observation pe-

riod. In our case, we assume that the insurance company will revert to

an initial strategy for auditing during the first period. This one is char-

acterized by a threshold value θ∗init, i.e., all incoming claims which exceed

this threshold are subject to verification whereas claims whose amount

is below this indicator will be indemnified right away. We denote this

specific auditing strategy by Ainit and define it formally as

Ainit = Ainit(θ∗init) = {θ|θ∗init ≤ θ}. (49)

Then, when having gathered enough information throughout the first

observation period, the insurer switches to the auditing range AR in the

consecutive periods.

3.3 Behavioral Adaptation

So far, the policyholders in the population who are likely and willing to

defraud were assumed to adhere to a constant fraud strategy. They chose

a constant multiplicative factor α and/or the same threshold value for

defrauding θ∗ph over the course of several periods. This constancy results

from the assumption that the policyholder population does not obtain

any information on the insurance company’s prevalent verification pro-

cess. Hence, there was no basis to give occasion for an adjustment of

their behavior. That also had an impact on the insurance company’s

corresponding optimal auditing strategy. As soon as the optimal veri-

fication process with respect to the prevalent defrauding behavior was

found, i.e., right after the first observation period, there was no need for

the insurance company to perform any adjustments to it. Summarizing,

no one of the participants in the insurance relationship had to change

their behavior.

However, it is realistic to assume that there might exist signals in-

dicating whether the insurance company changes its auditing strategy

in the subsequent period or not. Especially in the case of automobile

insurance, signaling is issued by (authorized) repair shops. Since dealing

3.3 Behavioral Adaptation 61

with a large number of insured events, they are able to estimate changes

in the auditing behavior of different insurance companies. In these cases,

the policyholders who are prone to defrauding would be given a chance

to change their fraud behavior and react to the new verification scheme.

In case the insurance company announces strengthened controls in order

to combat insurance claims fraud, the fraudulent part of the policyholder

population would choose to act more carefully in terms of their defraud-

ing strategy, i.e., lower the multiplicative factor α and/or their threshold

value for defrauding θ∗ph. In the opposite case, knowing that the insur-

ance company will relax their auditing scheme, it can be assumed that

attempts are made to exaggerate the actual loss amount θ even more and

obtain higher indemnification payments, i.e., by increasing α and/or θ∗ph.

Figure 7 gives an overview of the interaction between insurance com-

pany and (defrauding) policyholders and the resulting adjustment pro-

cesses of the respective behavioral strategies.

Both stakeholders define their respective initial strategy at the be-

ginning of the very first observation period in t = t0. For the insurance

company, this is its initial auditing strategy denoted by Ainit. Since by

that point in time, no information regarding the policyholders’ defraud-

ing strategy is available, it will be characterized by an initial threshold

value for auditing θ∗init. The policyholders themselves choose a claiming

scheme Θinit.9 In particular, the initial fraud strategy is defined by the

multiplicative factor α and an initial threshold value for defrauding θ∗ph,0(see Equation (45)). These two strategies are applied throughout the first

observation period [t0, t1]. At its end, in t = t1, all information with re-

gard to the actual distribution of the claimed losses throughout that

period as well as indications on the policyholders’ defrauding scheme,

i.e., the maximum value of detected fraud θmax,1 in [t0, t1], are avail-

able to the insurance company.10 Based on this information, the insurer

determines its optimal auditing strategy AR,1 for the first observation

9The function Θ includes the defrauding strategy for the dishonest policyholders(see Equation (45)).

10We assume that a sufficiently high number of audits has been performed duringthe course of the first period which has resulted in the detection of fraudulent claims,i.e., θmax,1 is observed.

62IITheoryofInsuranceFraud

t = t0 t = t1 t = t2

PH Θinit applied in [t0, t1]Θ(I(AR,1)) ...

applied in [t1, t2]Θ(I(AR,2))

IC Ainit

applied in [t0, t1]

ex-post optimization

AR,1

applied in [t1, t2]

ex-post optimization

AR,2 ...

θmax,1 I(AR,1) θmax,2 I(AR,2)

Figure 7: Interaction between Insurance Company (IC) and Policyholders (PH) over the Course of the FirstTwo Periods in an Insurance Relationship

3.4 Numerical Implementation of Iterative Optimization 63

period ex-post. The corresponding optimization problem is defined in

Equation (48). This adjusted auditing scheme will then be applied in the

second observation period [t1, t2]. At the same time, some signal I(AR,1)

concerning the adjustment of the verification process is communicated

to the policyholder population. They themselves now have the opportu-

nity to adapt their behavior accordingly. While the honest policyholders

adhere to reporting the actual loss amount when having suffered an in-

sured loss, the ones who are willing to defraud adjust their threshold

value for defrauding to θ∗ph,1. This new claiming scheme will be denoted

by Θ(I(AR,1)) and is applied in the second observation period [t1, t2].

However, the change in the defrauding behavior will be registered by the

insurance company in the form of a different maximum value of detected

fraud θmax,2 in the course of that second period. This new piece of in-

formation on the policyholders’ behavior induces once again an ex-post

optimization of the prevalent auditing strategy to AR,2 at the end of

this very period in t = t2. Again, the adjusted verification scheme AR,2

is applied in the following observation period after having provided the

policyholder population with a signal I(AR,2) concerning the change in

auditing. The interaction and adaptation processes can be repeated in

the same fashion over the course of several periods.

It needs to be emphasized that while we focus on the derivation of

the optimal auditing strategies AR,n, we also assure that all participants

are willing to maintain the insurance relationship, i.e., all participation

constraints as defined in Equations (38) and (43) need to hold when

applying the optimal verification process.

3.4 Numerical Implementation of Iterative

Optimization

In this subsection, we present the iterative approach regarding the opti-

mization of the auditing range AR,n in the nth period from the insurance

company perspective when interaction and hence adaptation is observ-


able.11

Step 1: Adjustment of claiming scheme We first consider the

policyholders’ claiming scheme Θn(θn, α, θ∗ph,n) is applied at the begin-

ning of each iteration. It is characterized by the defrauders’ strategy

indicated by a constant multiplicative factor α and a threshold value

for defrauding θ∗ph,n which is adjusted each period based on the signal

I(AR,n−1). In accordance to Equation (45), we obtain for the policy-

holders’ claiming scheme of the nth period

θn = Θn(θn, α, θ∗

ph,n) =

0 , no loss occurred

θn , no fraud or θn > θ∗ph,n

min{αθn, θ∗

ph,n} , fraud and θn < θ∗ph,n

, (50)

where θn represents a realization of the loss variable in the nth period.

The set consisting of all fraudulent claims associated with this strategy

is denoted by Fα,θ∗

ph,n.

Step 2: Determining maximum value of detected fraud The

next step to determining the optimal auditing strategy AR,n is the iden-

tification of the maximum fraud value which was actually detected in

the nth iteration, i.e., period. Apparently, it depends on the auditing

strategy AR,n−1 which was derived to be optimal in the (n− 1)th period

and is then applied in the nth period. Using the notation presented in

Equation (36), the maximum value of detected fraud in the nth period

can be defined as

θmax,n = max{θn · 1AR,n−1∩Fα,θ∗

ph,n

(θn)}. (51)

Step 3: Ex-post optimization of auditing strategy The value of

θmax,n forms the basis for the actual optimization process. Considering

11The subscripts n in the course of this subsection indicate the nth iteration process,i.e., the respective quantities for the nth observation period. Hereby, we consider alln ≥ 2. The special case of n = 1 corresponds to the initial period.

3.4 Numerical Implementation of Iterative Optimization 65

Equation (47), the insurance company’s auditing strategy for the nth

period is given by

AR,n ={

θn|θ∗R,n ≤ θn ≤ (1 + s) · θmax,n

}

, (52)

with s being the safety margin.

The aim is now to find the lower bound θ∗R,n of this audit range

such that the insurance company’s net present value of future cash flows

NPV is maximized and the stakeholders’ participation constraints hold:

maxθ∗

R,n

NPV (P, k, θ,Fα,θ∗

ph,n,AR,n)

NPVn ≥ 0

∆Un ≥ 0,

(53)

where ∆Un denotes the policyholders’ gain in expected utility from hav-

ing insurance coverage in the nth period.

Step 4: Communication of signal After having found the op-

timum value for the lower bound θ∗R,n of the auditing range, i.e., the

optimal auditing strategy AR,n, at the end of observation period n, a

signal I(AR,n) is communicated to the policyholder population inform-

ing about the adjustment of the prevalent verification scheme. For this

purpose, we define this signal as follows:

I(AR,n) =

(

θ∗R,n

θ∗R,n−1

+θmax,n

θmax,n−1

)

/2. (54)

This signal is used to adapt the claiming scheme Θn+1 at the be-

ginning of period n + 1. In this context, the signal I is an average of

two ratios: The first one represents the change of the upper bound from

period n− 1 to n whereas the second one constitutes the change of the

maximum value of detected fraud from period n− 1 to n.


4 Simulation Results

In Sections 2 and 3, we have presented a model framework and poten-

tial optimal auditing strategies when interaction between policyholder

and insurance company and consequently behavioral adaptation over

the course of several observation periods is possible. In this section, we

present and analyze the corresponding numerical solutions for the opti-

mal auditing strategy from the insurance company perspective.

4.1 Parametrization of the Reference Setting

In our simulations, we consider a policyholder population consisting of

M = 2′500′000 individuals. An assumed probability of loss occurrence

of π = 0.2 leads to N = 500′000 loss realizations of θ per observation

period. Hereby, the latter follow a log-normal distribution. This assump-

tion is commonly used as mentioned in Marlin (1984) since it guarantees

positive values for the realizations of the random variable. In particular,

the expected value E(θ) is set µ = 1 and the variance V ar(θ) = σ2 = 0.4.

All individuals among the population are assumed to be risk averse. For

instance, their risk aversion parameter a is considered to be 6. Further-

more, the policyholders’ initial wealth position is set W = 0. At the

same time, the individuals have to pay an insurance premium P at the

beginning of each observation period. The latter can be split up into

the fair premium and an appropriate loading factor. The fair premium

corresponds to the expected loss. Hence, having set the expected value

of the loss variable θ to µ = 1 and considering the probability of suffering

a loss to be π = 0.2, this implies a fair premium of 0.2. However, since

the insurance company faces additional costs, it will add a correspond-

ing loading factor to the fair premium. As mentioned in Cummins and

Mahul (2004), the loading factor can not be too large since potential

policyholders would not sign the insurance contract under such condi-

tions. For our analyses, we will assume the total insurance premium

to be P = 0.3. Furthermore, the cost per audit is set k = 0.05 which

corresponds to 16.67% of the insurance premium P . For the purpose of

our analyses, we will disregard costs other than the ones due to auditing.

4.2 Simulation Results and Sensitivity Analyses 67

The share of fraud-prone policyholders among the population is assigned

the value p = 0.2, i.e., 20% of all policyholders who suffer an insured loss

may exaggerate that amount if it is in accordance with their defrauding

strategy. Their defrauding strategy is accompanied by the choice of the

relative fraud amount α and/or an appropriate threshold value for de-

frauding θ∗ph. To start with, we take α to be 2, i.e., the policyholders

who decide to defraud report back an amount twice as high as the actual

loss amount. However, in case the individuals have a threshold value for

defrauding as described in Section 3.1, they never claim more than that

value θ∗ph. For the purpose of our analyses, we assume θ∗ph = 1.1 which

is 10% higher than the expected value of the loss variable. Finally, the

insurance company needs to decide on the parameters concerning its au-

diting strategy A. During the very first period, it opts for a verification

process Ainit which is characterized by a threshold value for auditing

θ∗init, we set its initial value to 1 which corresponds to the expected value

of the loss variable θ. As already explained at the end of Section 3.2,

information with regard to the policyholders’ defrauding behavior needs

to be gathered first before being able to apply this verification scheme

AR. Hence, we initially set θ∗init = 1, and determine the paramters θmax

and θ∗R based on the information obtained based on the first program

run. With regard to the upper bound of the auditing range, the value

for the safety margin s is assumed to be 0.1, i.e., the upper bound of the

auditing range is 10% higher than maximum of detected fraud θmax. The

resulting auditing range AR is then applied in a consecutive program run.

Table 2 sums up the choices for the input parameters for the reference

setting as introduced above. In the course of this and the following

sections, we base our simulations and studies on these values.

4.2 Simulation Results and Sensitivity Analyses

The remainder of this section constitutes the presentation and discus-

sion of the simulation results. For the simulations, we adhere to the

parameter choice presented in Table 2 unless noted otherwise.


Input parameter Reference level

Total number of policyholders M 2’500’000

Number of loss realizations N 500’000

Loss distribution θ lnN (1, 0.4)

Insurance premium P 0.3

Share of fraud-prone policyholders p 0.2

Relative fraud amount α 2

Initial threshold value for auditing θ∗

init 1

Safety margin s 0.1

Policyholder’s initial threshold θ∗

ph,0 1.1

Auditing cost k 0.05

Risk aversion parameter a 6

Table 2: Input Parameters for the Reference Setting

4.2.1 Development of Optimization Results Over Several

Iterations

In this subsection, we present and discuss the development of the optimal

auditing range AR over the course of several iterations. Furthermore, we

analyze its impact on quantities like the number of performed audits, the

amount of fraudulent claims, the net present value NPV and the gain

in utility ∆U . To get a better insight of the effects, we consider both the

parametrization of the reference setting with costs per audit k = 0.05

as well as the case when the costs per audit are raised to k = 0.3 and

compare the results.

Development of Optimal Auditing Range AR

Comparing Figure 8(a) with Figure 8(b), we can see that higher costs per

audit k result in a slightly broader optimal auditing range AR, i.e., the

share of values which may be verified becomes greater. At the same time,

the optimal auditing range shifts in an upward direction, i.e., the value

of the claims which may be subject to auditing becomes higher. For the

insurance company this implies that, in case of high expenditures per

case, they should focus their investigations on those claim which exhibit

high saving potential whenever an engagement in fraudulent activities is

detected.


2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

number of periods

θ*R

θmax

θ*ph

(a) Development of Optimal AuditingStrategy, k = 0.05

2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

number of periods

θ*R

θmax

θ*ph

(b) Development of Optimal AuditingStrategy, k = 0.3

Figure 8: Development of the Optimal Auditing Strategy throughoutthe Course of several IterationsThe development is displayed for two different choices of cost per audit k respectively. Theremaining parameters are chosen as presented in Table 2.

From the policyholder perspective, we find that higher costs per audit

k lead to a higher threshold of defrauding θ∗ph, i.e., the value up to which

policyholders take build-ups into consideration increases. This observa-

tion shows that the cost per audit does not only have an impact on the

insurance companies auditing strategy but indirectly also on the policy-

holders’ behavior, in particular on their defrauding strategy. Since the

insurer signals an upward shift in his verification behavior, policyholders

(and the corresponding service providers) are left with the impression

that inflating a loss amount up to some value is more likely to remain

undetected than in the previous period. In return, they then raise their

threshold value for defrauding.

Development of Number of Performed Audits and Fraudulent

Claims

We measure both the number of performed audits and the number of

fraudulent claims in relation to the total number of filed claims.

Figure 9(a) confirms the intuition that higher costs per audit k result

in a lower share of incoming claims which are subject to verification,

i.e., fewer auditing processes are performed. As mentioned above, this


2 4 6 8 10

010

20

30

40

50

number of periods

num

ber

of audits (

in %

)

2 4 6 8 10

010

20

30

40

50

number of periods

num

ber

of audits (

in %

)

k=0.05

k=0.3

(a) Development of the number ofaudits performed by the insurancecompany when applying the optimalauditing strategy for the respectiveperiod.

2 4 6 8 10

05

10

15

20

number of periods

num

ber

of fr

aud (

in %

)

2 4 6 8 10

05

10

15

20

number of periods

num

ber

of fr

aud (

in %

)

k=0.05

k=0.3

(b) Development of the number offraudulent claims when the insurancecompany applies the optimal auditingstrategy for the respective period.

Figure 9: Development of Number of Audits and the Number of Fraud-ulent Claims over the Course of Several IterationsBoth quantities are measured in relation to the total number of losses, i.e., filed claims. Thedevelopment is illustrated for two different choices of the cost per audit k. The remainingparameters are chosen as presented in Table 2.

restriction in the number of verification processes leads the insurance

companies to focus on those claims which, in case of detected fraud,

have a higher saving potential, i.e., higher valued claims.

From the policyholder point of view, the number of fraudulent claims

consequently increases (see Figure 9(b)). This finding is in line with our

results presented in Figure 8. Due to receiving a signal indicating an

upward shift, the policyholders themselves raise their threshold value

for defrauding. As a consequence of this elevation, the number of losses

below the threshold increases resulting in more cases where actions are

taken to inflate the claim amount.

It needs to be noted that even though 20% of the policyholder pop-

ulation are willing to exaggerate their loss amount, the real numbers lie

below that value (see Figure 9(b)). This phenomenon can be explained

with the existence of the threshold value for defrauding θ∗ph up to which

fraud is actually taken into consideration. The actual share of build-

up among all claims may depend on different factors. As already seen

in Figure 8, higher costs per audit k result in an increased defrauding

threshold θ∗ph. This, however, implies a higher likelihood of the actual


loss amount being below the threshold value. As a consequence, the

amount of fraud may increase up to the maximum of 20%.

Development of Net Present Value NPV and Gain in

Utility ∆U

2 4 6 8 102 4 6 8 102 4 6 8 102 4 6 8 10

0.2

0.4

0.6

number of periods

NPV k=0.05

NPV k=0.3

∆U k=0.05

∆U k=0.3

Figure 10: Development of the Insurance Company’s Net Present Valueand the Policyholders’ Gain in Utility over the Course of Several Itera-tionsFor each period, the optimal auditing strategy is applied. The development is illustratedfor two different choices of the cost per audit k. The remaining parameters are chosen aspresented in Table 2.

Looking at Figure 10, it strikes attention that both NPV and ∆U

are positive for both chosen values of the cost per audit k. Especially

with regard to gain in utility ∆U , this implies that the policyholders

among the population are willing to adhere to the insurance relationship

(see Equation (43)). This observation proves that the derived optimal

auditing schemes are feasible from both stakeholders’ perspectives.

From the insurance company point of view, higher costs per audit

k lead to a lower net present value NPV . This phenomenon may be

explained by the fact that higher auditing costs result in fewer auditing

processes (see Figure 9(a)) but in a higher share of fraudulent claims

(see Figure 9(b)). As a consequence, more exaggerated claim amounts

remain undetected resulting in higher, unjustified expenses from the in-

surance company perspective.


Another intriguing result can be taken from Figure 10 recalling the

case where behavioral adaption is not possible. Since in that simplified

setting signals are not exchanged, no changes in both the auditing and

the claiming strategy would be possible, resulting in a stable solution

after period two. Comparing the values from the second observation

period with the consecutive ones in Figure 10, we see that, given the

current setting, from the policyholder point of view, the gain in utility

in the second observation period is considerably higher than the ones

in all the consecutive observation periods, implying that the option to

change ones strategy is disadvantageous to them. This result is very

enlightening since it contradicts the widespread opinion that adapting

the defrauding strategy based on signals especially from third parties

like service providers is favorable from the individuals perspective.

4.2.2 Sensitivity Analyses

The remainder of this section constitutes the presentation and discussion

the impact of relevant input parameters have on the insurance company’s

optimal auditing strategy AR and the resulting effects on the net present

value NPV . In particular, the influence of the cost per audit k, the

relative fraud amount α and the policyholder’s initial threshold value

θ∗ph will be analyzed respectively.

For this purpose, we consider the final values of the optimal audit-

ing range AR, net present value NPV and gain in utility ∆U after 12

iterations each when stable results are achieved.

Cost Per Audit

We take k ∈ [0.05, 0.5] and illustrate the results for the auditing range as

well as the corresponding values for the insurance company’s net present

value NPV in Figure 11 keeping the remaining parameters as presented

in Table 2.

Figure 11(a) shows that a change in the cost per audit k merely

has an impact on the width of the auditing range. However, the values

themselves which trigger the verification process shift upwards for higher

values of this specific input parameter. The higher the cost per audit k


0.1 0.2 0.3 0.4 0.5

0.0

0.5

1.0

1.5

2.0

0.1 0.2 0.3 0.4 0.5

0.0

0.5

1.0

1.5

2.0

cost per audit k

θ*R

θmax

(a) Auditing Range Depending onCost Per Audit k

0.1 0.2 0.3 0.4 0.5

0.0

0.2

0.4

0.6

0.8

0.1 0.2 0.3 0.4 0.5

0.0

0.2

0.4

0.6

0.8

cost per audit k

∆ U

NPV

(b) Corresponding Values for ∆U andNPV

Figure 11: Auditing Range and the Corresponding Objective Quantitiesfrom Insurance Company and Policyholder Depending on the Cost PerAudit kThe remaining parameters are chosen as presented in Table 2.

is, the higher are the claim amounts which will be subject to auditing.

These findings are in line with the ones presented in Figure 8. The lower

the costs per audit are, the more verification processes the insurance

company can perform assuming a given budget. This allows the insurer

to review a larger number of incoming claims and consequently enhances

the probability of revealing the fraudulent ones, in particular those which

are close to the policyholders’ threshold value. Such an approach enables

the insurance company to adjust its auditing strategy optimally to the

prevalent defrauding behavior at an early stage. As a consequence, po-

tential escalations with regard to the fraud strategies, i.e., expansion of

the policyholder’s individual threshold value, can be prevented. In this

context, note that the upper bound of the audit range in Figure 11(a)

which is defined by the maximum values of detected fraud, is decreasing

when lowering the costs per audit k.

From the policyholder perspective, we observe that the gain in utility

∆U is always positive, implying that the auditing strategies discussed

above are feasible.


Relative Fraud Amount

Considering α ∈ [0.25, 2.5], we illustrate the effects on the optimal audit-

ing strategy AR in Figure 12 and discuss them afterwards. Again, the

remaining input parameters are chosen as given in Table 2.

0.5 1.0 1.5 2.0 2.5

0.0

0.5

1.0

1.5

2.0

0.5 1.0 1.5 2.0 2.5

0.0

0.5

1.0

1.5

2.0

relative fraud amount α

θ*R

θmax

(a) Auditing Range DependingRelative Fraud Amount α

0.5 1.0 1.5 2.0 2.50.0

0.2

0.4

0.6

0.8

0.5 1.0 1.5 2.0 2.50.0

0.2

0.4

0.6

0.8

relative fraud amount α

∆ U

NPV


Figure 12: Auditing Range and the Corresponding Objective Quantitiesfrom Insurance Company and Policyholder Depending on the RelativeFraud Amount αThe remaining parameters are chosen as presented in Table 2.

As can be seen in Figure 12(a), the relative fraud amount α has a con-

siderable impact on the insurance company’s optimal auditing strategy.

The width of the auditing range increases (slightly) for greater values of

this input parameter. At the same time, the claim values which indicate

the necessity of verification shift in an upward direction. As a result,

the relative fraud amount α also has an impact on both stakeholders’

objective quantities. Figure 12(b) illustrates that the insurance com-

pany’s net present value NPV is increasing when raising the values of

this input parameter. The reason for this observation is that in case of a

successful verification process, i.e., the detection of fraudulent behavior,

the relative fraud amount α will become known. The higher the relative

fraud amount α is - while assuming the loss distribution itself has not

changed - the more profitable it is from the insurance company perspec-

tive to audit claims which demand high indemnity payments. Hence,

the relative fraud amount α has a direct influence on the upper bound

of the auditing range. This observation gets even clearer when keeping


in mind that the latter is determined by the maximum of all detected

fraudulent claims during one period.

Furthermore, Figure 12(b) shows that the insurance company prof-

its from raising and widening the auditing range whenever the relative

fraud amount α is increased. In this current scenario, the relative fraud

amount α is raised while keeping the probability for fraudulent behavior

p constant, i.e., fraud is not committed more often but more severely.

Since the loss distribution remains unchanged, this implies that fraud-

ulent claims are more likely to be the higher valued ones. From the

insurance company perspective this means that auditing becomes more

profitable when shifting its auditing range into this area. Since in the

case of detected fraudulent behavior no indemnity payments to the pol-

icyholder are made, this auditing strategy has a positive effect on the

insurance company’s net present value NPV .

Again, we see that the policyholder’s gain in utility ∆U is positive

throughout all observation periods guaranteeing that the corresponding

auditing strategies are feasible.

Policyholder’s Initial Threshold

The final input parameter whose influence on the insurance company’s

optimal auditing strategy we aim to analyze is the policyholders’ initial

threshold value θ∗ph. This values serves as an upper bound for the poten-

tial fraud amount. As already introduced in Section 3.1, policyholders

who decide to commit fraud exaggerate their loss amount by some con-

stant factor α up to that threshold value θ∗ph. For the purpose of our

sensitivity analysis, we consider θ∗ph ∈ [1.05, 1.5] and present the results

in Figure 13.

Figure 13 illustrates that the choice of the policyholders’ threshold

value for defrauding θ∗ph has a significant impact on the optimal auditing

range AR. Higher values of θ∗ph imply an increasing discrepancy with re-

gard to the insurance company’s initial threshold for auditing θ∗init which

is kept at a constant value of 1.0. As a result, the optimal auditing range

AR becomes broader for increasing values of θ∗ph. In particular, the upper

bound of the auditing range is continuously increasing while the lower

bound remains almost constant. The explanation for this phenomenon


1.1 1.2 1.3 1.4 1.5

0.0

0.5

1.0

1.5

2.0

1.1 1.2 1.3 1.4 1.5

0.0

0.5

1.0

1.5

2.0

threshold for defrauding θ*ph

θ*R

θmax

(a) Auditing Range Depending on

Policyholder’s Initial Threshold θ∗ph

1.1 1.2 1.3 1.4 1.5

0.0

0.2

0.4

0.6

0.8

1.1 1.2 1.3 1.4 1.5

0.0

0.2

0.4

0.6

0.8

threshold for defrauding θ*ph

∆ U

NPV


Figure 13: Auditing Range and the Corresponding Objective Quantitiesfrom Insurance Company and Policyholder Depending on the Policy-

holder’s Initial Threshold Value θ∗phThe remaining parameters are chosen as presented in Table 2.

is that a raise in the policyholders’ defrauding threshold θ∗ph results in

an increase in the share of fraudulent claims among all filed claims. In

particular, the amount of exaggerated claims among the higher-valued

ones will increase. Since the upper bound of the optimal auditing range

is determined as the maximum of detected fraud θmax and some safety

margin s, its value will become higher as well.

This explanation can also be used for understanding the resulting

marginal increase in the insurance company’s net present value NPV .

Since higher values of θ∗ph lead to an increased likelihood of a loss amount

being below this threshold, the number of cases where fraud-prone poli-

cyholders engage in build-up rises, especially in the high-value segment.

Whether this development has an impact on the insurance company’s

net present value depends on the prevalent auditing strategy AR and

its detection success. Interpreting Figure 13(b), the number of detected

fraudulent activities increases compared to the number of unjustifiably

paid out claims resulting in fewer indemnification which in turn leads to

a slightly higher net present value.

Like in the previous analyses, the gain in utility ∆U from having

signed an insurance contract prior to the occurrence of loss is always

positive implying that all participation constraints are met.

5 Critical Discussion 77

5 Critical Discussion

The insurance company’s optimal auditing strategies derived in this pa-

per are characterized by two threshold values indicating the range of

claimed values which should be subject to verification. All the other in-

coming claims are indemnified without further particular proof of their

truthfulness. In particular, the presented approach results in examin-

ing claims especially from the medium segment leaving out small and

high-valued ones. This strategy is based on the assumption that pol-

icyholders avoid any engagement in fraudulent activities whenever the

actual loss amount is above some personal threshold since they fear the

probability of being caught to be particularly high in this segment. As

a consequence, theoretically there is no need to verify incoming claims

of higher magnitude.

From a practical point of view, however, this approach appears to

be incomplete. It seems unimaginable that insurance companies indem-

nify loss amounts which are far above the corresponding expected value

without further examination of their legitimization. For this purpose,

we once more extend our model framework to accommodate this aspect.

We therefore introduce an additional threshold value for auditing, θ∗high.

In addition to verifying all incoming claims whose value fall withing the

auditing range AR, the insurance company also audits those which are

above the new threshold value θ∗high.

In order to depict the impact of adding an additional threshold value

to the existent auditing range AR, we consider θ∗high = 1.5 which equals

one and a half the expected value of the loss amount θ. The remaining

parameters are chosen as in the reference setting. Figure 14 illustrates

the results.

As can be seen from Figure 14, in the particular setting of our model

framework, an additional auditing threshold identifying high-valued claims

for verification does not generate benefit for the insurance company. The

optimal auditing range AR including the additional threshold θ∗high re-

sults in a net present value of NPV = 0.118 after the tenth observation


2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

number of periods

θ*R

θmax

θ*ph

(a) Auditing Range with Additional

Auditing Threshold θ∗high

= 1.5

2 4 6 8 102 4 6 8 10

0.2

0.4

0.6

number of periods

NPV

∆U


Figure 14: Auditing Range Including an Additional Auditing Thresholdand the Corresponding Objective QuantitiesThe additional auditing threshold θ∗

high = 1.5 is displayed as well as the correspondingobjective quantities from insurance company and policyholder perspective. The remainingparameters are chosen as presented in Table 2.

period, whereas the optimal auditing range AR alone in NPV = 0.120,

i.e., we obtain a change of 2%. From the policyholder perspective, the

introduction of the new threshold value θ∗high has no impact. The gain

in utility ∆U remains positive.

This observation can be explained by the underlying defrauding be-

havior of the policyholders. Since fraud-prone individuals do no inflate

loss amounts in this segment, the insurer performs costly auditing pro-

cesses without ever detecting any fraudulent activities, i.e., additional

costs arise without ever leading to savings due to refusal of indemnifica-

tion. As a consequence, the insurance company’s net present value NPV

decreases when introducing the additional threshold value for auditing

high-valued claims. From the policyholder perspective, no changes in

the gain in utility arise since the new auditing scheme has no impact on

the indemnification payments.

In practice, however, this observation does not necessarily have to

hold true. On the one hand, policyholders and/or service providers

might indeed engage in fraudulent activities in case of high-valued losses

or even if no insured loss occurred at all. As an example, Emerson

(1992) recapitulates the case ”State vs. Book” in which the policyholder

6 Conclusion 79

exaggerated the value of his stolen luxury class automobile by 20%. On

the other hand, insurance companies might profit from performing ver-

ification processes even in those cases when no fraudulent activities are

detected. Their investigations might have a deterrent effect discouraging

policyholders and service providers to dare fraud attempts in the future.

The corresponding monetary benefits, however, are almost impossible to

measure (see, e.g., Viaene and Dedene (2004)).

6 Conclusion

In this paper, we develop a model framework which depicts an optimal

auditing scheme with regard to inflated insurance claims. The key ele-

ment in this context is the auditing range which - triggered by the filed

amount - selects those claims which should be subject to verification.

Its actual configuration is chosen in way that maximizes the insurance

company’s position while at the same time maintaining contract attrac-

tiveness such that policyholders are willing to adhere to the insurance

relationship. In addition, we incorporate the possibility for each stake-

holder to adapt its behavioral strategy over the course of several periods.

By this means, we take into consideration that changes in the policy-

holder defrauding behavior have a crucial impact on the optimal corre-

sponding auditing strategy and vice versa. Insurance companies may

use their experiences from previous verification processes as a source of

information whereas policyholders often rely on third parties like service

providers.

One of our main findings is the derivation of the optimal auditing

scheme characterized by a range whose exact boundaries we are able

to calculate. We come to the conclusion that given some constant cost

per audit it is optimal to verify the truthfulness of claims from the mid-

value segment. In particular, it is not reasonable from the insurance

company point of view to examine small claims since the accompanying

costs outweigh the savings potential in case of detected fraud. Not ver-

ifying high-valued claims results from the assumption that fraud-prone

policyholders do not inflate the magnitude of their losses above some


personal threshold value since they fear that the likelihood of getting

caught in this segment to be above-average. Omitting this assumption,

however, may require the introduction of an additional threshold value

for auditing.

Furthermore, we are able to show that while the option to adapt one’s

strategy might be favorable from the insurance company perspective, it

actually has a negative impact on the policyholders’ position compared

to the situation where no signals are exchanged based on which one

could change its behavior. This result is astonishing since it disproves

the common believe that adapting the defrauding strategy with the help

of signal from service providers would be advantageous from the policy-

holder point of view.

Using a numerical approach based on Monte Carlo simulations, we

are able to illustrate and analyze the impact of different parametrizations

on the optimal auditing range. High costs per audit as well as a high

relative fraud amount result in an upward shift of the auditing range,

whereas an increase in the policyholders’ defrauding threshold leads to

broadening the range. With regard to the insurance company’s objective

quantity, the relative fraud amount has a particularly strong impact on

its result.

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85

Part III

The Identification of

Insurance Fraud:

An Empirical Analysis

Abstract

Fraud is a major concern in the insurance industry. Time after time,

spectacular incidents become public of individuals trying to scam tremen-

dous indemnifications from their insurance companies. The majority of

claims, however, particularly those seeking low to medium indemnifica-

tion, exhibit no obvious signs of fraudulent activity thereby leading the

insurer to believe they were legitimate. In this study, we therefore fo-

cus on determining the characteristics that make an accurate distinction

between fraudulent and legitimate claims possible. In addition to iden-

tifying dishonest cases more systematically, applying a criteria catalog

would enable an efficient use of the limited resources with which fraud

investigation divisions are usually endowed. The basis of our analysis

is established by a comprehensive data set of automobile claims from a

large Swiss insurance company collected throughout the years of 2004

to 2011. The results of the logistic regression analyses reveal different

relevant determinants on the policyholder, vehicle, policy and loss level.

Contrary to common assumptions, it is most often individuals with a

flawless driving record possessing high-valued cars who decide to de-

fraud their insurance company. In extension, we place special focus on

how the amount of loss affects an individual’s likelihood of engaging in

fraudulent activities.12

12K. Muller. The Identification of Insurance Fraud - An Empirical Analysis. Work-

ing Papers on Risk Management and Insurance, 2013.This paper has been presented at the 2013 Annual Conference of the Asia-PacificRisk and Insurance Association in July 2013.

86 III Empirical Analyses

1 Introduction

Insurance fraud has been a key concern in the industry ever since. To

date, particularly astonishing incidents have regularly made headlines

involving tremendous illegitimate indemnifications from insurance com-

panies. These cases, however, may just be the tip of the iceberg. Ac-

cording to a report by the Association of British Insurers (2012), 15

fraud attempts are being detected each hour of every day, summing up

to 139,000 cases worth nearly 1 billion GBP in the United Kingdom in

the year of 2011. Even though insurance companies and related organiza-

tions take numerous measures to combat this wide-spread phenomenon,

due to its secretive nature, a major part of fraud goes undetected, result-

ing in an estimated total of another 2 billion of excess payments each

year in the United Kingdom (see Association of British Insurers (2012)).

In light of its prevalence and economic extent, several insurance com-

panies established their own investigative units to uncover insurance

fraud. Being equipped with limited budgets, however, they are forced to

verify only those claims which exhibit a comparatively high probability

of containing fraud and a relatively high saving potential rather than an-

alyzing every single incoming claim. A recent survey conducted by Coali-

tion Against Insurance Fraud (2012) among 74 mostly property/casualty

insurers revealed that 88% of the respondents employ technologies to sup-

port their investigators, two of the most common being “automated red

flags” and “scoring capabilities”.

Nevertheless, many insurers are just beginning to discover the neces-

sity of establishing fraud investigation divisions within their own com-

pany. Interviews with experts in this field have revealed that, in particu-

lar, smaller insurance companies may not deem it worthwhile to invest in

costly software, still relying on their intuition when it comes to detecting

fraudulent claims.

Our aim is, hence, to identify the determinants that would make

it possible to draw conclusions on the likelihood of a claim seeking un-

founded indemnification. Based on such a catalog of criteria, insurance

companies would be able to use their limited resources to reveal defraud-

1 Introduction 87

ing attempts more effectively. In addition, honest policyholders may

also benefit from an improved auditing scheme and hit ratio. Processing

times would likely shorten, thereby resulting in reduced waiting periods

for indemnification.

With the aim of detecting insurance fraud by engaging in auditing

processes, the insurance companies’ strategy can be assigned to the cate-

gory of costly state verification (see, e.g., Townsend (1979), Mookherjee

and Png (1989), Bond and Crocker (1997), Picard and Fagart (1999),

Dionne, Giuliano, and Picard (2009)). The latter is based on the as-

sumption of information regarding the (allegedly) insured event being

distributed asymmetrically between the policyholder and the respective

insurance company. It is, therefore, possible that the policyholder may

misrepresent facts and figures in order to obtain a higher or even un-

justified indemnification. To confront and discourage any defrauding

attempts, insurance companies perform verification processes to deter-

mine the truthfulness of incoming claims and may then choose to impose

penalties. Since audits, however, incur costs and the respective divisions

have limited funds at their disposal, a choice must be made as to which

of the incoming claims to test. An important consideration in this con-

text is the weighing of incurred costs against potential savings related

to detected fraud attempts.

An alternative approach in the handling of insurance fraud is sub-

sumed under the term costly state falsification (see, e.g., Crocker and

Morgan (1998), Crocker and Tennyson (2002)). Other than in the first-

mentioned one, the idea behind this approach is for the policyholder

to be able to manipulate a claim at monetary expense such that the

fraud attempt becomes undetectable. In this case, auditing proves to be

obsolete, leaving the insurer with the potential option of indemnifying

all incoming claims without further verification while at the same time

raising the premium payments. This approach would be in line with the

findings of Clarke (1989) and Morley, Ball, and Ormerod (2006), who re-

vealed that insurance companies were concerned with reputational risks

as a consequence of excessive auditing. Such an approach could create

a negative image in public perception, as a result of which individuals


may be tempted to switch to one of the company’s competitors.

For the purpose of our study, we will use the term “fraud” or “fraud

attempt” as a collective term for all those cases within our data sample

for which the respective insurance company has found sufficient evidence

to categorize them as such. The phenomenon of insurance fraud having

many facets, there is a variety of forms that may be observed in this con-

text (see, e.g., Picard (2001), Crocker and Tennyson (2002), Tennyson

(2008)).

Based on the severity of the offense, a common distinction is made

between soft fraud and criminal/ hard fraud. According to Derrig (2002),

criminal fraud is defined as the “willful act of obtaining money or value

from an insurer under false pretenses or material misrepresentations”.

Expert interviews as well as previous research (see, e.g., Weisberg and

Derrig (1991), Viaene and Dedene (2004), Tennyson (2008)), however,

have revealed that the majority of defrauding attempts is situated in

an ethical gray area rather than containing outright fraud. Even in the

absence of a definition, the term soft fraud is related to attempts to

inflate the claims amount after the occurrence of an insured event in

order to obtain higher indemnification.

Aside from policyholders, other potential actors associated with the

occurrence of insurance fraud include insurance brokers, intermediaries

and service providers (see, e.g., Dulleck and Kerschbamer (2006) and

International Association of Insurance Supervisors (2011)). Whether it

is charging excessive prices or providing unnecessary services and treat-

ments, such activities can be performed either with or without the knowl-

edge of the respective policyholder aiming to obtain additional payments

from the insurance company (see Tennyson (2008)).

The aim of our study is to identify the determinants that help to ac-

curately distinguish between legitimate and illegitimate incoming claims.

Hereby, we take into account characteristics regarding the policyholder

himself, the insured vehicle, the signed policy and the loss event itself.

1 Introduction 89

Previous literature has analyzed potential indicators that predict

the likelihood of fraud by employing discrete choice models.13 For the

specifics of the US insurance market, Tennyson and Salsas-Forn (2002)

as well as Derrig, Johnston, and Sprinkel (2006) analyze the phenomenon

of insurance fraud related to automobile personal injuries requiring med-

ical treatment. While the latter present some exemplary measures to

handle fraud attempts, Tennyson and Salsas-Forn (2002) find that au-

diting processes contain both a detection and a deterrence component.

Furthermore, Belhadji, Dionne, and Tarkhani (2000) identify fraud in-

dicators to determine their actual impact on the fraud probability of a

claim using a representative data set from Canadian insurance compa-

nies. A slightly different path in this context is followed Dionne et al.

(2009). Using the scoring approach, they derive a red flag strategy indi-

cating which of the suspicious claims should be referred to an external

investigative units. The result is an optimal auditing strategy in the face

of a cost-minimizing insurance company.

Apart from that, Artıs, Ayuso, and Guillen (1999), Artıs, Ayuso,

and Guillen (2002), Caudill, Ayuso, and Guillen (2005), Pinquet, Ayuso,

and Guillen (2007) and Bermudez, Perez, Ayuso, Gomez, and Vazquez

(2008) address potential issues which may surface in relation to the data

sample itself. These include selection biases based on the insurers’ own

criteria for selecting claims to undergo auditing in the first place (see

Pinquet et al. (2007)) and oversampling of fraudulent claims in the data

set (see Artıs et al. (1999) and Bermudez et al. (2008)). Furthermore,

Artıs et al. (2002) and Caudill et al. (2005) account for misrepresenta-

tion of honest claims, i.e., cases that the insurance company mistakenly

considers as legitimate.

With this paper, we aim to extend the existing studies on the identifi-

cation of insurance fraud. Based on the literature, we develop a number

of hypotheses to gain new insights into the drivers of fraudulent behavior.

Furthermore, we utilize of a comprehensive data set from the automobile

13For different approaches to determining fraud indicators see, e.g., Derrig, Weis-berg, and Chen (1994) and Brockett, Derrig, Golden, Levine, and Alpert (2002). Ai,Brockett, Golden, and Guillen (2013) use such indicators to determine the overallfraud rate in a population of filed claims.


insurance market in Switzerland. To the best of our knowledge, such an

analysis on indicators predicting the existence of insurance fraud has not

been performed for the Swiss market to date.

The data sample we acquired for our analysis is comprised of au-

dited claims from a major Swiss insurance company. The audits were

performed throughout the time period between 2004 and 2011 within

their automobile devision. Potential fraud indicators are available on

the policyholder, vehicle, policy and loss level. By applying logistic re-

gression methods, we determine which characteristics have a significant

impact on the occurrence of fraud and could therefore be used to trigger

auditing processes.

One particular interesting result refers to the impact of the insured

loss amount on the policyholder’s decision to engage in fraudulent activ-

ities. We are able to show that the option to defraud one’s insurance

company is solely taken into consideration for comparably small loss

amounts, proving that behavioral adaption in the context of insurance

fraud does take place.

Particularly from a practical perspective, the identification of factors

revealing the probability of defrauding attempts is crucial. Being able to

assess the fraud potential of an incoming claim is an essential step in the

claims settlement process. Since the resources that are set aside to com-

bat insurance fraud are limited, it is of great importance to distinguish

between those claims for which verification is deemed sensible and those

which should be paid out right away. This paper’s derived catalog of

criteria can serve as a basis for implementing auditing strategies to han-

dle defrauding attempts more effectively. The extent to which insurance

companies make use of this information, however, depends particularly

on their available budgets.

The remainder of this paper is structured as follows: Section 2 sets

forth ten hypotheses with regard to potential fraud indicators and their

respective effect on the likelihood of committing fraud. We then provide

a comprehensive overview of our data sample using descriptive measures,

before presenting our theoretical model. The results of the logistic re-

2 Theory and Hypotheses Development 91

gressions are reported and discussed in Section 3. Finally, in Section 4,

we summarize our findings and provide an outlook for future research.

2 Theory and Hypotheses Development

2.1 Development of Hypotheses

In the following, we develop several hypotheses with regard to the de-

terminants that may serve as potential fraud indicators revealing the

probability of an incoming claim being untruthful. Using data from

auto insurance policies of a Swiss insurance company, we take into con-

sideration characteristics on the policyholder, vehicle, policy and loss

level.

Previous literature has already analyzed suitable indicators in the

context of insurance claims fraud. In our study, we pick up the pre-

sented research results to examine whether or not the fraudulent claims

in our data sample exhibit the same characteristics. In addition, several

additional hypotheses are introduced which, to the best of our knowl-

edge, have not yet been tested empirically.

Fraud Indicators Based on Policyholder Characteristics

Policyholder Age According to a representative population survey

commissioned by the German Insurance Association GDV (2011), there

is a wide-spread perception among all age groups that defrauding one’s

insurance company would generally be easy. A closer look, however,

reveals this attitude to be slightly more prevalent among younger policy-

holders than older ones. Similarly, a study published by the Insurance

Fraud Bureau (2012) reveals that while 8% of all survey participants

stated their willingness to participate in a staged accident for financial

profit, this number increases to 14% among young people. One reason

behind this attitude may be that financial benefits from successful fraud

attempts carry more weight for younger policyholders than for older ones

due to their respective average assets. These elaborations are also in line

with the findings of Artıs et al. (2002) who show in their data sample


that younger drivers are more likely to try to defraud their insurance

company. Therefore, we hypothesize:

H1: The younger the policyholders are, the more likely they

are to engage in fraudulent activities.

Fraud Indicators Based on Vehicle Characteristics

Vehicle age In connection with characteristics related to the insured

vehicle itself, its age may be of interest to predicting the probability of

a claim being fraudulent. Artıs et al. (2002) were able to prove this link,

empirically showing that older vehicles are more likely to be involved in

fraudulent activities since policyholders may perceive its cash value as a

form of additional funds when purchasing a new car. Following this line

of reasoning, one can assume fraud in this context not only to occur in

the form of build-up, but also as seeking indemnification for uninsured

events in order to gain financial benefits. We include this aspect in our

study, and hypothesize:

H2: The older vehicles are, the more likely they are to be

involved in insurance claims fraud.

Vehicle type Additionally, the vehicle’s class may be associated with

a particular probability of being involved in fraudulent activities. In our

data set, we can distinguish between regular passenger cars, transporters

and motorcycles. Insurers have long been known to take the vehicle class

into account when pricing the policy since it serves as an indicator for

driving behavior and related accident frequency. Therefore, we include

this variable in our analysis and postulate:

H3: The class of an insured vehicle has a significant impact

on the probability of filing a fraudulent claim.

Vehicle value Another characteristic related to the vehicle’s charac-

teristics is its value, which is composed of its catalog price and the value

of any accessories, such as audio systems, car phones or air conditioning.

In particular, these additions, whether fitted already by manufacturer or

2.1 Development of Hypotheses 93

at some later point, have the potential to substantially increase the in-

sured vehicle’s value the consequence being higher insurance premiums.

As policyholders then have financial incentives to engage in fraudulent

activities, we aim to verify the following hypothesis within our data sam-

ple:

H4: The higher the value of an insured vehicle, the more

likely defrauding attempts become.

Leasing More and more individuals are choosing to lease their au-

tomobiles instead of purchasing them. A recent representative study

in Switzerland commissioned by comparis.ch (2011), the leading Swiss

Internet comparison service, revealed that the share of leased vehicles

accounts for 14% of the overall private automobile market. This number

rises even up to 23% with regard to the share of leased cars among all

new private ones. With an average price of 42,328 CHF, leased cars are,

on average, slightly more expensive than those paid for in cash costing

40,091 CHF. Leasing contracts usually provide the lessee with the right

to purchase the then-used vehicle at the end of contract. Since the price

is generally determined already by the time of signing the leasing agree-

ment, it is in the lessee’s interest to obtain the car in its best possible

condition. This, however, may incentivize individuals to misuse their in-

surance coverage, to eliminate defects of any kind at the expense of the

insurance company. As a consequence, one could expect the magnitude

of claims to be disproportionally high for leased vehicles. Therefore, we

hypothesize:

H5: Leased vehicles are more likely to be engaged in fraudu-

lent activities than purchased ones.

Fraud Indicators Based on Policy Characteristics

Loss-free An individual’s perception of insurance in general may

serve as an incentive in the context of fraud. Surveys have discovered

that policyholders perceive build-up in particular as a way to obtain

a compensation for former premium payments without having made

a claim (see, e.g., International Association of Insurance Supervisors


(2011), Miyazaki (2008), Duffield and Grabosky (2001)). This attitude

adopts the common idea of treating insurance as an investment which

has to eventually pay off. Consequently, we expect policyholders who

have been in an insurance relationship for several periods without filing

a claim to use the opportunity to inflate the amount of an insured loss

by the time of its occurrence. We therefore postulate:

H6: The longer the insurance relationship exists while re-

maining loss-free, the more likely defrauding attempts become.

Records In the context of automobile insurance, most insurance

companies offer their policyholders bonus-malus policies providing them

an incentive not to file claims for all kinds of minor losses and at the

same time rewarding them for accident-free driving records (see, e.g.,

Moreno, Vazquez, and Watt (2006)). We believe that bonus-malus poli-

cies may be an obstacle in filing a claim to begin with, particularly for

small damages. Since, however, it implies negative consequences for the

policyholder in the form of increased premium payments for the consec-

utive period, this penalty may at the same time provide an incentive

to obtain additional payments from a claim in order to compensate for

additional future expenses. This kind of attitude is expected to be par-

ticularly observable among individuals having a bad driving record since

they already are likely to be at the highest premium level. In these cases,

Artıs et al. (1999) argue that the claimants may feel like they have “noth-

ing to lose” anyway. Based on their data sample, Artıs et al. (1999) are

able to show that the number of previous claims indeed has an impact

on the likelihood of a fraud attempt. We therefore aim to verify the

following:

H7: The higher the number of previous claims, the higher the

likelihood of a claim containing fraud.

Fraud Indicators Based on Loss Characteristics

Type of damage In discussions with experts from several fraud

investigation divisions, attention was drawn to the different types of


damages for which policyholders file claims. Particular focus was placed

on loss events whose magnitude may easily be manipulated by either

“overprovision” or “overcharging” (see Tennyson (2008)) as well as to

damages that are allegedly difficult to verify and, hence may encour-

age defrauding attempts. These include, among others, glass breakage

and collisions. Therefore, we include this variable in our analysis and

postulate:

H8: Types of damages which are deemed to be difficult to

verify (e.g., glass breakage and collisions) are more likely to

contain fraud than those which are deemed easily verifiable.

Loss amount In filing a fraudulent claim, its magnitude is of partic-

ular importance. We are convinced that policyholders do have a presen-

timent of the existence of auditing and hence take it into consideration

when engaging in fraudulent activities. With claims of high magnitude

being supposedly one of the targets under investigation, we expect fraud

prone policyholders to contemplate such actions solely in cases of smaller-

valued loss events and in the form of a percental surcharge on the actual

loss amount. This approach would additionally leave the option to ex-

cuse any incorrect claims as a mistake if audited by the insurance com-

pany(see, e.g., Emerson (1992)). Hence, we hypothesize the following:

H9: Smaller-valued claims are more likely to contain some

kind of fraud than higher valued ones.

Delay Previous studies have shown (see, e.g., Artıs et al. (2002),

Dionne et al. (2009)) that the longer the lag between the accident and

the filing of a report to the insurance company, the higher the likelihood

of the respective claim containing some kind of fraud. The reason be-

hind this observation is assumed to be that policyholders take this time

to elaborate on the alleged story that they are trying to sell to their in-

surance company. We therefore include this aspect in our analysis, and

postulate:

H10: Greater delay in reporting an event to the insurance

company increases the probability of fraud attempts being un-

dertaken.


2.2 Data Set

Our data set is constituted of personal-, vehicle-, policy- and loss-related

information on the population in the automobile insurance division of

a Swiss insurance company. It is comprised of all claims filed between

the years of 2004 and 2011, summing up to a total of 1, 429, 896 claims

seeking for almost 2.5 bn CHF in indemnification. Throughout this time

period, 7, 407 (0.52 percent) of those claims were examined by the com-

pany’s fraud investigation division. The indemnification payments for

these cases summed up to a total of more than 60 mn CHF. Among the

7, 407 audited claims, 402 (5.43 percent) were identified as fraudulent,

mainly exhibiting signs of build-up. Consequently, the majority of these

claims received some partial indemnification, only 1.49 percent of them

were denied any payment.

As indicated previously, we make use of the word “fraud” as a col-

lective term for all cases that were categorized as such by the insurance

company. This, however, does not imply that every single one of these

cases is an offense in the criminal-law sense. Judging from the high

amount of partial indemnifications, the majority of audited claims seems

to have exaggerated the actual loss amount rather than completely forg-

ing an insured loss event. Hence, these cases would fall into the category

of soft and not criminal fraud. Nevertheless, in our study we choose

not to make a distinction regarding the extent to which the individuals

defrauded the insurance company.

Furthermore, we do not differentiate between the potential actors in

the context of insurance fraud. However, besides the policyholders them-

selves, third parties like repair shops may also be involved in fraudulent

activities. On the one hand, the initiative may be taken by the insured

hoping for previous damages, unrelated to the current accident, to get

repaired. On the other hand, the repair shops may be the ones to inflate

the loss amount, either by charging overly high prices or providing unnec-

essary services (see Tennyson (2008)). These actions can be undertaken

with or without the knowledge of the policyholder.

2.2 Data Set 97

Data Selection

The insurance company’s decision as to whether an incoming claiming

has to undergo verification or not was based on personal evaluation of the

incoming cases. The investigation division consists primarily of employ-

ees with a police background having broad experience with fraudulent

activities in the insurance context. A predefined set of fraud indica-

tors, however, that may serve as hints for the probability of fraud being

present in a claim, had not existed during the time period between 2004

and 2011.

Nevertheless, it can be expected that the investigators did not pro-

ceed arbitrarily. Being aware of the limited resources at their disposal,

they sought to focus on those claims that appeared to have a high

probability of being illegitimate and that exhibited a high saving po-

tential. Even in the absence of a predefined set of selection criteria, they

likely chose the claims for auditing accordingly. These criteria, however,

whether chosen deliberately or not, may influence the composition of

our data sample of audited claims and therefore impact the results of

the regression analyses.

For this purpose, we report measures on sample composition for the

sample of all filed claims as well as the subsamples of audited and not

audited claims. The results can be found in Tables 13 and 14 in the Ap-

pendix. According to the results, investigators seem to have selected dis-

proportionally young policyholders who drive either older or high-valued

vehicles. They exhibited flawless driving records, however by the time

of loss occurrence, seeking comparably high indemnification. Regarding

the type of damage, cases reporting the theft of the insured vehicle seem

to have been the target of investigations.

Selection bias being probably present to some extent, we nevertheless

perform our analyses to identify potential fraud indicators. Insurance

companies being driven by the need to minimize their cost and time

consumption, it seems unrealistic to expect anyone to perform auditing

on a completely random basis. We will therefore not be able to acquire

a data sample that is free of all selection biases.


2.3 Descriptive Statistics

In this section, we present descriptive measures to provide insight into

the full data samples of audited claims as well as the subsamples of

fraudulent and legitimate ones. Tables 3 and 4 give an overview of all

variables used in our analysis.

The first column in Table 3 shows the mean and standard deviation

for a number of policyholder-, vehicle-, policy- as well as loss-related

characteristics for the overall data set. Policyholders whose claims had

to undergo verification were on average just over 39 years old. The

vehicles involved in the loss events were a little over 7 years of age, being

worth more than 48, 000 CHF including accessories. While the claimants

had remained loss-free for over 4 consecutive years, their driving records

were comprised of 3 previous loss events. On average, it took insured

individuals almost 16 days to file a claim after the loss event occurred,

seeking over 8, 700 CHF of indemnification.

The second and third columns in Table 3 specify this information for

the subsamples of fraudulent and legitimate claims in order to uncover

potential differences between these two groups. To identify whether any

discrepancies are the result of significant differences between the sub-

samples or simply arise randomly, we perform a two-sample t-test for

the equality of the means (see p-values). While policyholders proven

to have engaged in fraudulent activities were on average over 40 years

old, honest ones were nearly two years younger. With the corresponding

p-value of the t-test being 0.0111, i.e., less than 0.05, this observation

may be a hint that the policyholder’s age serves as an indicator of the

existence of fraud. Regarding their vehicles, it is striking that those par-

ticipate in a defrauding attempt were approximately one year younger

but almost 4000 CHF more expensive than those in the opposing group.

Again, taking the results of the t-test into account, these variables might

allow us to draw conclusions on the probability of fraud. Furthermore,

in terms of driving behavior, there seem to be significant differences

between the two subsamples. Claimants belonging to the group of de-

frauders have remained loss-free for almost one year longer and, at the

same time, were involved in fewer accidents during the whole duration

2.3

Descrip

tive

Statistics

99

Audited Claims Defrauders Non-defrauders

mean s.d. mean s.d. mean s.d. p-value

N=7407 N=402 N=7005

Policyholder age 39.18 13.87 40.78 12.52 39.09 13.94 0.0111

Vehicle age 7.39 5.75 6.54 4.68 7.43 5.80 0.0004

Vehicle Value (CHF) 48,313 59,250 51,929 39,809 48,105 60,171 0.0707

No. consec. loss-free years 4.26 2.33 4.84 2.53 4.22 2.31 < 0.0001

No. previous records 3.18 7.55 2.11 1.84 3.24 7.75 < 0.0001

Loss amount (CHF) 8,711 16,996 5,379 12,088 8,847 17,153 < 0.0001

Delay in filing claim (days) 15.90 43.61 13.23 35.39 16.06 44.05 0.1462

Table 3: Descriptive Statistics for the Sample CompositionThis table reports the mean and standard deviation (s.d.) of different characteristics related to policyholder, vehicle, policy and loss withregard to the full sample of audited claims. This information is narrowed down particularly for the two subsamples of proven fraud attempts(i.e., defrauders) and legitimate claims (i.e., non-defrauders). Furthermore, the last two columns provide the results of a two-sample t-test.


of their insurance relationship. Surprisingly, however, by the time of the

loss occurrence, fraud-prone policyholders claimed loss events totaling

to a little more than half the cost of that of their honest counter parts.

Lastly, we observe that the delay in filing a claim appears to be irrelevant

when predicting the probability of fraud.

Table 4 provides further information on the composition of the data

set. Similarly to Table 3, we report the number and percentages of

characteristics on the policyholder, vehicle, policy and loss level for the

data set of audited claims in column one, and specify this information

for the subsamples of fraudulent and legitimate claims in columns two

and three respectively.

Comprising 58.90 percent of the whole population, Swiss citizens ac-

counted for the majority of all policyholders. This number drops slightly

(to 44.53 percent) among the subsample of fraud-prone claimants. While

the greater portion of the overall policyholder population (72.09 percent)

had their place of residence in the German-speaking part of Switzerland,

only 22.82 percent indicated that their place of residence was among the

French-speaking cantons of Switzerland and merely 5.09 percent in the

Italian-speaking part.14 These numbers do not seem to change consid-

erably when comparing the subsamples of fraudulent and honest indi-

viduals. With respect to vehicle-related characteristics, we report the

vehicle type and whether the latter was leased or not. A majority of

about 71 percent of all policyholders had insurance coverage for a regu-

lar passenger car. This number rises by almost seven percentage points

among the subsample of defrauding claimants. The opposite holds true

for motorcyclists among the population. While their share among all

claimants sums to 23.36 percent, they only account for 16.04 percent of

all detected fraud attempts. Transporters form the smallest part of all

vehicle types comprising around 5.30 percent of the overall data sample

as well as within the two subsamples. While less than 19 percent of all in-

sured vehicles were leased, they account for about 30 percent of all cases

14Based on the prevalent quantity, the Swiss cantons are allocated as follows: Ticinoto the Italian-speaking part, Geneva, Vaud, Neuchatel, Jura and Fribourg to theFrench-speaking part and the remaining cantons to the German-speaking part.

2.3 Descriptive Statistics 101

Audited Claims Defrauders Non-defrauders

No. Percent No. Percent No. Percent

Policyholder related characteristics

Citizenship

Swiss 4363 58.90 179 44.53 4184 59.73

other 3044 41.10 223 55.47 2821 40.27

Total 7407 100.00 402 100.00 7005 100.00

Area of residence

German-speaking part 5313 72.09 282 70.15 5031 72.20

French-speaking part 1682 22.82 83 20.65 1599 22.95

Italian-speaking part 375 5.09 37 9.20 338 4.85

Total 7370 100.00 402 100.00 6968 100.00

Vehicle related characteristics

Vehicle type

Car 3525 71.34 210 78.36 3315 70.94

Transport 262 5.30 15 5.60 247 5.29

Motorcycle 1145 23.36 43 16.04 1111 23.77

Total 4941 100.00 268 100.00 4673 100.00

Leasing

Leased 1404 18.96 123 30.60 1281 18.29

Not leased 6003 81.04 279 69.40 5724 81.71

Total 7407 100.00 402 100.00 7005 100.00

Policy related characteristics

Bonus protection clause

Included 2991 40.38 203 50.50 2788 39.80

Not included 4416 59.62 199 49.50 4217 60.20

Total 7407 100.00 402 100.00 7005 100.00

Loss related characteristics

Type of damage

Theft 2437 32.90 100 24.86 2337 33.36

Glass 1130 15.25 25 6.22 1105 15.77

Collision 1368 18.71 124 30.85 1244 17.76

Others 2472 33.37 153 38.06 2319 33.10

Total 7407 100.00 402 100.00 7005 100.00

Table 4: Descriptive Statistics for the Sample CompositionThis table describes the sample composition using different categorical variables on thepolicyholder, vehicle, policy and loss level. Besides providing an overview of the completedata sample of audited claims, the information is further differentiated with regard tofraudulent (i.e., defrauders) and legitimate (i.e., non-defrauders) claims.


proven to have engaged in fraudulent activities. Additionally, we pro-

vide information as to whether the policyholders had included a bonus

protection clause in their contracts or not. This holds true for about 40

percent of the whole population, and over 50 percent among the subsam-

ple of detected defrauders. Finally, with respect to the claimed loss type,

we distinguish between theft of the vehicle, glass breakage, collision and

other damages.15 Almost one third (32.90 percent) of all audited claims

had reported the theft of the insured vehicle, whereas glass breakage and

collision accounted for approximately 15 and 19 percent of all incidents,

respectively. The shares of theft and glass breakage, however, drop no-

tably by eight percentage points each within the subsample of fraudulent

claims, while the portion of cases including collisions rises by more than

twelve percentage points.

2.4 Model Derivation

The aim of our study is to identify the impact a set of explanatory

(predictor) variables has on a dichotomous (binary) dependent variable,

i.e., taking on solely one of the two values - one and zero (fraud and no

fraud). We are hence envisaging the possibility of employing the logistic

regression model.

In this relation, let us consider the following linear regression model:

yi = β0 + β1xi1 + β2xi2 + . . . + βmxim + ǫi = xiβ + ǫi (55)

where yi denotes the outcome of the dependent variable for the ith claim,

i.e., fraud or no fraud, and xim represents the value of the mth explana-

tory variable for the ith claim. Furthermore, βm specifies the regression

coefficients to be estimated, with β0 being the intercept, and the ran-

dom variables ǫi indicate the error terms. Having a system of linear

equations, one may also abbreviate by using matrix notation. Hereby,

xi is a column vector with each row containing the values of the ex-

planatory variables for the ith claim, and β a column vector with the

15The sub-category “others” comprises, among others, damages caused by hail,martens and other wild life, parking damages and theft of valuable left in the vehicle.

3 Empirical Results 103

corresponding regression coefficients.

In contrast to linear regression models, however, the logistic regres-

sion does not pursue the estimation of the dependent variable’s outcome

yi itself, but rather its probability of occurrence πi which is defined as

πi = Prob(yi = 1) = E(yi) since yi is dichotomous, i.e., Bernoulli dis-

tributed. Applying this to Equation (55), we obtain

πi = xiβ, (56)

since E(ǫi) = 0 for all i. This equation is commonly referred to as linear

probability model.

Unfortunately, applying the ordinary least squares (OLS) method

for estimating the regression coefficients βi, as usually done in relation

to linear regression models, would give rise to a series of problems in

this context. It may predict values outside the permitted range of [0, 1],

and is not able to capture heteroscedasticity and non-normality of error

terms arising with dichotomous dependent variables (see, e.g., Pohlmann

and Leitner (2003)). In addition to all this, utilizing OLS may produce

nonsensical predictions for the estimation results. These obstacles can

be overcome by drawing on the logistic model, which makes use of the

logistic function Prob(z) = 1/(1 + exp(−z)). With Equation 56, this

results in

πi = Prob(xiβ) =1

1 + exp(−xiβ). (57)

In this case, the regression coefficients βi, also referred to as logit coef-

ficients, are derived by means of maximum likelihood estimation (MLE).

Its aim is to determine those parameter values βi, which make the ob-

servation of the collected data yi and xi the most likely.

3 Empirical Results

In this section, we present and discuss the results of the logistic regression

model introduced previously. Hereby, we begin with the set of explana-

tory variables with regard to policyholder characteristics and extend this


initial model stepwise by adding the variables on the vehicle, policy and

loss level in each iteration, respectively.

In order to compare the different models against each another and ul-

timately to assess how well the final model actually fits the observations,

we present different measures of model adequacy.

3.1 Logistic Regression Results

Model 1: Policyholder Characteristics

The first model considers only the influence that the policyholder

characteristics introduced in Tables 3 and 4 have on the decision to de-

fraud the insurance company or not. Results of the logistic regression

are reported in Table 5.

N = 7002 βi exp(βi) s.e. p-value sig.

Constant –3.5406 0.0290 0.1798 < 0.0001 ***

Policyholder age 0.0098 1.0098 0.0038 0.0104 *

citizenship:other 0.6718 1.9578 0.1067 < 0.0001 ***

area of residence:fr –0.1945 0.8232 0.1338 0.1461

area of residence:it 0.4960 1.6421 0.1926 0.0100 *

Table 5: Logistic Regression with Determinants Related to PolicyholderCharacteristics (Model 1)Results for the logistic regression of the dependent variable (fraud/no fraud) with threeexplanatory variables on the policyholder level (plus constant). The regression coefficientsβi indicate the contribution of each explanatory variable on the logit, exp(βi) the corre-sponding effect on the odds ratio, and s.e. represents the standard error of the respectivedeterminant. Significance levels (sig.): *** = 0.1 percent, ** = 1 percent, * = 5 percent,. = 10 percent.

As already indicated by the result of the two-sample t-test in Table 3,

the claimant’s age has a significant effect on the likelihood of engaging

in fraudulent activities (p < .05). The respective regression coefficient

being positive, older policyholders are more fraud prone than younger

ones (β = .01). This confirms our assumption that the policyholder age

is indeed an indicator for detecting fraud, however, it contradicts H1.

3.1 Logistic Regression Results 105

Furthermore, we find both citizenship and area of residence to be

statistically significant. In particular, claimants not having the Swiss

citizenship appear to be more involved in dishonest activities than their

counter-group (β = .67, p < .0001). With regard to the categorical

variable area of residence, we use all policyholders living in the German-

speaking part of Switzerland as a reference group. While individuals

from the French-speaking cantons do not exhibit significantly different

defrauding behavior (β = −.19, p > .1) compared to the German-

speaking ones, claimants from the Italian-speaking part have a higher

probability of engaging in fraudulent activities (β = .50, p < .05).

Model 2: Policyholder and Vehicle Characteristics

In addition to the policyholder characteristics, the second model

takes the variables on the vehicle level into account (see Tables 3 and

4). The results of the corresponding logistic regression can be found in

Table 6.


Constant –2.772 0.0625 0.2694 < 0.0001 ***

policyholder age 0.0059 1.0059 0.0047 0.2060



area of residence:it 0.3551 1.4263 0.2204 0.1071

vehicle age –0.0296 0.9708 0.0201 0.1424

vehicle type:transporter –0.0852 0.9183 0.3231 0.7920

vehicle type:motorcycle –0.3243 0.7230 0.0208 0.1196

Vehicle value 0.0001 1.0000 0.0001 0.9459

leasing:no –0.4962 0.6088 0.1512 0.0010 **

Table 6: Logistic Regression with Determinants Related to Policyholderand Vehicle Characteristics (Model 2)Results for the logistic regression of the dependent variable (fraud/no fraud) with fourexplanatory variables on the vehicle level in addition to the three policyholder charac-teristics (plus constant). The regression coefficients βi indicate the contribution of eachexplanatory variable on the logit, exp(βi) the corresponding effect on the odds ratio, ands.e. represents the standard error of the respective determinant. Significance levels (sig.):*** = 0.1 percent, ** = 1 percent, * = 5 percent, . = 10 percent.


Examining the regression coefficients and p-values for the policy-

holder characteristics, we find that result from Model 1 regarding the

impact of citizenship is confirmed.

Furthermore, we see that, in this model set up, the vehicle’s age may

not serve as an indicator for fraud being prevalent in a claim (β = −.03.

p > .1). With regard to vehicle type, the reference group is comprised

of all cases where a regular passenger car was involved in the loss event.

In comparison, neither transporters (β = −.09, p > .1) nor motorcy-

clists (β = −.32, p > .1) exhibited a significantly different defrauding

behavior than drivers of passenger cars. The criterion of whether the ve-

hicle was leased or not seems to be a good indicator of fraud (β = −.50,

p < .005). With the regression coefficient being negative, we can con-

clude that owners of non-leased vehicles are less tempted to defraud the

insurance company. This finding supports the assumption stated in hy-

pothesis H5. Surprisingly, however, the vehicle’s value does not appear

to be statistically significant for the existence of fraud (p > .1).

To evaluate whether extending the initial Model 1 by the variables

on the vehicle level improves the fit, we conduct a likelihood ratio test.

The results are reported in Table 9. According to the corresponding val-

ues (χ2 = 24.7, p < .0001), Model 2’s fit proves to be significantly better.

Model 3: Policyholder, Vehicle and Policy Characteristics

The next step in extending our model is to additionally include all

variables on the policy level. Table 7 shows the corresponding results.

With regard to the parameters already included in Models 1 and 2,

we see that our previous results are confirmed. The explanatory variables

on the policyholder and vehicle level remain significant with respect to

the prediction of the likelihood of fraud.

Both the number of consecutive loss-free years and the number of

previous records seem to be statistically significant in predicting the

probability of fraud. In particular, claimants who remained loss-free for

a longer time period are more likely to get involved in fraudulent activi-



Constant –2.6110 0.0735 0.3580 < 0.0001 ***

policyholder age 0.0063 1.0063 0.0048 0.1859



area of residence:it 0.3675 1.4441 0.2243 0.1014

vehicle age –0.0151 0.9850 0.0184 0.4097

vehicle type:transporter –0.0529 0.9485 0.3254 0.8709

vehicle type:motorcycle –0.5520 0.5758 0.2117 0.0091 **

vehicle value 0.0001 1.0000 0.0001 0.6818

leasing:no –0.5370 0.5845 0.1505 0.0003 ***

No. consecutive loss-free years 0.0664 1.0687 0.0280 0.0178 *

No. previous records –0.2506 0.7783 0.0422 < 0.0001 ***

bonus protection clause 0.3362 1.3996 0.1360 0.0134 *

Table 7: Logistic Regression with Determinants Related to Policyholder,Vehicle and Policy Characteristics (Model 3)Results for the logistic regression of the dependent variable (fraud/no fraud) with threeexplanatory variables on the policy level in addition to the three policyholder and fourvehicle characteristics (plus constant). The regression coefficients βi indicate the contribu-tion of each explanatory variable on the logit, exp(βi) the corresponding effect on the oddsratio, and s.e. represents the standard error of the respective determinant. Significancelevels (sig.): *** = 0.1 percent, ** = 1 percent, * = 5 percent, . = 10 percent.

ties once they experience an insured loss event (β = .07, p < .01). This

result provides proof for hypothesis H6. Regarding driving records, we

find that the less previous claims a policyholder has had the higher the

likelihood of defrauding the insurance company (β = −.25, p < .0001).

On the one hand side, this observation is consistent with the result from

the number of consecutive loss-free years. On the other hand side, it

seems counter-intuitive since a high driving record is associated with in-

dividuals having a bad and/or insecure driving behavior and therefore is

deemed to be a predictor for the likelihood of fraud. Another indicator

for the presence of fraud in a claim is the information whether a bonus

protection clause was included in the insurance contract or not. Accord-

ing to the results of the logistic regression, policyholders who included

this option in their contracts were involved in fraudulent activities more

often than their counter-group (β = .34, p < .05).


The results of the likelihood ratio test of Model 3 against Model 2,

presented in Table 9, confirm that the addition of the variables on the

policy level does help to significantly increase the predictive accuracy

(χ2 = 29.10, p < .0001).

Model 4: Policyholder, Vehicle, Policy and Loss

Characteristics

Our final Model 4 reflects the effect of all variables on the predictabil-

ity of fraud being present in a claim. The results are presented in Table 8.


Constant –2.2030 0.1105 0.4343 < 0.0001 ***

Policyholder age 0.0097 1.0097 0.0054 0.0793 .

citizenship:other 0.4635 1.5896 0.1519 0.0023 **

area of residence:fr 0.1347 1.1442 0.1879 0.4734

area of residence:it 0.6636 1.9418 0.2555 0.0094 **

vehicle age –0.0214 0.9788 0.0233 0.3585

vehicle type:transporter 0.2390 1.2700 0.3505 0.4954

vehicle type: motorcycle –0.6660 0.5138 0.2768 0.0161 *

vehicle value 0.0001 1.0000 0.0001 0.0006 ***

leasing:no –0.7682 0.4638 0.1774 < 0.0001 ***

no. consecutive loss-free years –0.0011 0.9989 0.0337 0.9728

no. previous records –0.2206 0.8020 0.0460 < 0.0001 ***

bonus protection clause 0.0065 1.0065 0.1661 0.9688

type of damage:glas –2.3110 0.0992 0.5363 < 0.0001 ***

type of damage:collision 0.4653 1.5925 0.2096 0.0264 *

type of damage:other –0.1971 0.8211 0.2125 0.3535

loss amount –0.0001 0.9999 0.0001 < 0.0001 ***

delay in filing claim –0.0077 0.9923 0.0035 0.0284 *

Table 8: Logistic Regression with Determinants Related to Policyholder,Vehicle, Policy and Loss Characteristics (Model 4)Results for the logistic regression of the dependent variable (fraud/no fraud) with threeexplanatory variables on the loss level in addition to the three policyholder, four vehicleand three policy characteristics (plus constant). The regression coefficients βi indicate thecontribution of each explanatory variable on the logit, exp(βi) the corresponding effecton the odds ratio, and s.e. represents the standard error of the respective determinant.Significance levels (sig.): *** = 0.1 percent, ** = 1 percent, * = 5 percent, . = 10 percent.

Starting with the loss characteristics, we find the magnitude of loss

amount to be highly significant for filing fraudulent claims (p < .0001).


The regression coefficient being negative implies that the smaller the loss

amount, the more likely the existence of fraud. This observation was al-

ready indicated by the results from the two-sample t-test in Table 3 and

provides proof for our predication stated in hypothesis H9. The outcome

for the delay in filing a claim, however, seems surprising. Even though

its effect on the dependent variable is significant (p < .05), the negative

sign of β = −.01 suggests that the shorter the time lag between the

occurrence of loss and the report to the insurance company, the higher

the likelihood for fraud. This is directly contrary to our assumption ex-

pressed in H10. A possible explanation may be that, like in the case with

the loss amount, claimants do suspect the insurance company to control

for the delay in filing a claim and hence not only take the magnitude of

loss into consideration when defrauding, but also manipulate the date of

loss occurrence whenever it is possible. Once more, the aim is to feign

realistic scenarios in order to not get audited and moreover detected.

On the policyholder level, the final model confirms some of the effects

already predicted in Model 1: Older claimants have a higher probability

of cheating on their insurance company. This observation, however, con-

tradicts our assumption in hypothesis H1. Put in the context of driving

behavior and premium payments to date, a potential explanation may

be that it is actually the older and thus (usually) more experienced poli-

cyholders who remain loss-free throughout long periods of time. Having

paid insurance premiums over the course of many years, they may con-

sider themselves long-standing customers who expect good will in form

of generous indemnification in trade for their loyalty.

Regarding the variables related to the vehicle itself, the fully extended

model once again confirms previous results: Both the vehicle value and

the information whether the vehicle is leased or not are very good indica-

tors for fraudulent claims. The proven effects support our assumptions

expressed in hypotheses H4 and H5 respectively. Furthermore, we are

able to show that the vehicle class has an impact on the likelihood of

fraud, motorcyclists cheating less on the insurance company than drivers

of regular passenger cars (see H3). Solely, hypothesis H2 does not hold

true. Against our prediction, the age of the insured vehicle does not


seem to have an impact on the likelihood to engage in fraudulent activi-

ties (β = −.02, p > .1).

Also, from the policy perspective, the results from Model 3 prove

to be true: Exhibiting a small number of previous claims increases the

likelihood of inflating the loss magnitude once an insured event occurs.

In comparison with Model 3, the fully extended Model 4 leads to a

significantly better fit according to the likelihood ratio test in Table 9

(χ2 = 106.55, p < .0001), indicating that the fully extended Model 4 is

to be preferred over the less evolved ones.

∆χ2 ∆df χ2 df p-value sig.

Model 1 1651.1 4858

Model 2 1626.4 4854 24.69 4 < 0.0001 ***

Model 3 1597.3 4850 29.10 4 < 0.0001 ***

Model 4 1490.8 4845 106.55 5 < 0.0001 ***

Table 9: Likelihood Ratio Tests for the ModelsResults of the pairwise likelihood ratio tests between the consecutive Models 1 to 4. Eachextension of the previous model leads to a significant improvement in fit as indicatedby the increasing values for χ2 and the corresponding p-values. Significance levels (sig.):*** = 0.1 percent, ** = 1 percent, * = 5 percent, . = 10 percent.

Having decided on the final model for identifying fraud indicators,

i.e., Model 4, we conclude this section by assessing its adequacy.

To check for potential problems with regard to the multicollinearity

of independent variables within our data set, we determine their variance

inflation factors, which can be found in greater detail in Table 12 in the

Appendix. The fact that their values do not exceed the critical threshold

value, the highest being 1.59 for the variable vehicle type, indicates that

it is reasonable to assume our explanatory variables to be uncorrelated.

Table 10 displays the classification table for the full logistic regression

model using all explanatory variables in our data set. The results confirm

the good predictive accuracy of our model. In particular, with regard to

the number of fraudulent claims, we are able to predict 73.76 percent cor-

rectly.This number, however, decreases slightly to 67.97 percent with re-

spect to predicting the cases of legitimate claims. These figures indicate

3.2 Special Focus on Loss Amount 111

that our model is slightly more suitable for detecting fraudulent claims

than honest ones. Apparently, many of the characteristics that help to

identify fraudulent claims are also present among legitimate claims. On

the one hand, the small number of detected fraudulent claims may be

to blame. Only 402 out of the 7,407 audited claims (5.43 percent) were

classified as fraudulent, making these cases rare events. On the other

hand, our data sample was restricted to those criteria which are solely

assumed to be helpful with respect to fraud detection. In light of this,

there may exist other explanatory variables besides those included in

our data sample, which may improve the distinction between honest and

dishonest claims. These may include many determinants already known

to the insurance company, but also some that have not been gathered

yet.

Predicted

Observed Fraud No Fraud % Correct

Fraud 149 53 73.76

No Fraud 1493 3168 67.97

Table 10: Classification Table for Full ModelThis classification table illustrates the predictive accuracy of the logistic regression modelin Table 8 by showing how many of the observed values for the dependent variable (fraud/no fraud) are correctly predicted. The full model correctly predicts 73.76 percent of thefraud attempts and 67.97 percent of the legitimate claims.

3.2 Special Focus on Loss Amount

As already revealed in the course of this section, fraud-prone policyhold-

ers do take the loss amount into consideration when deciding whether

to actually engage in fraudulent activities or not. More precisely, the

results of the logistic regression model as presented in Table 8 indicate

that the two are inversely proportional to each other, i.e., actions to ob-

tain higher indemnification tend to be undertaken when the insured loss

amount is comparably small.

In this subsection, we focus on this particular fraud indicator and

discuss its effect on the decision to cheat one’s insurance company. For


this purpose, Figure 15 illustrates the link between loss amount and the

likelihood of fraud being present in an incoming claim. It must be noted

that, for the purpose of this analysis, we consider solely the loss amount

as a factor for predicting the existence of fraud. While taking other

significant exploratory variables into account would certainly increase

the overall accuracy in detecting defrauding attempts (see Table 10), it

would not impact the link between the loss amount’s magnitude and the

likelihood of fraud.

Loss Amount

0.0

0.2

0.4

0.6

0.8

1.0

20000 60000 100000 140000

Figure 15: Contribution of Loss Amount to Predicting the Likelihood ofFraudThis figure illustrates both the actual magnitudes of loss events for honest and dishonestclaims within our data sample as well as the loss amount’s overall effect on the likelihoodof fraud. While the blue line indicates the predicted probability of fraud depending on themagnitude of loss, each of the black points represents the loss amount of an actual claimfrom the data set, the corresponding y-value hinting fraud (1) or no fraud (0).

In Figure 15, we include the audited cases from our data set exhibit-

ing a loss amount up to 150000 CHF. Each of the points in the figure

depicts one claim within our data sample in terms of the corresponding

loss amount and the information as to whether fraud was detected or

not. Secondly, we add the predicted effect of the magnitude of a loss

3.2 Special Focus on Loss Amount 113

event on the likelihood to commit fraud, represented by the blue line in

Figure 15.

This demonstates that, with regard to the honest claims, the loss

amounts vary greatly across a wide range of magnitudes, reaching values

of 150000 CHF and higher. For cases proven to be illegitimate, however,

the contrary holds true. Here, the loss amounts seem concentrated in the

range of up to 20000 CHF, occasionally going up as far as 40000 CHF.

This observation is reflected by the predicted effect on the likelihood of

fraud being involved in a claim. The blue line indicates that, while for

small magnitudes,the loss amount accounts for almost ten percent of the

predictability of fraud being present, this value drops rapidly to zero

percent for loss amounts higher than 50000 CHF.

This leads us to conclude that defrauding attempts are not consid-

ered an option if the insured loss amount exceeds some threshold value.

Primarily for relatively small magnitudes, some individuals may try to

obtain higher indemnification payments from their insurance companies.

This observation provides proof for behavioral adaptation in the con-

text of insurance fraud. Fraud-prone policyholders can be expected to

adjust their defrauding schemes in such a way that their attempts remain

undetected. Previous research has already shown that individuals fear

negative consequences in the form of losses as a result of their actions

more than they would appreciate a gain of the same size (see, e.g., Kah-

neman and Tversky (1979), Kerr (2012)). Hence, the overall objective

is deemed to be perceived as presenting a legitimate claim rather than

solely “maximizing” indemnity payments. Additional evidence for this

link can be found, e.g., in Viaene, Derrig, Baesens, and Dedene (2002)

and Tennyson (2008) who state that while only very few claims contain

outright fraud, the majority of defrauding attempts is detected in cases

seeking low to medium amounts of indemnification.


4 Conclusion and Critical Discussion

With fraud being identified as one of the central challenges in the indus-

try to date and in the future, many insurance companies have established

their own investigation divisions in the recent years. Nevertheless, many

still rely largely on intuition when it comes to detecting wrongful claims.

In our study, we identify criteria that allow for an accurate distinction

between fraud-prone and honest policyholders and, by this means, pre-

dict the existence of fraud in a filed claim. Such a catalog of variables

allows for a systematic approach to the combat against fraud, hopefully

resulting in a higher detection rate. Moreover, it enables a targeted uti-

lization of the limited resources that investigation divisions have at their

disposal.

Our analysis is based on a sample of claims data comprised of 7,407

audited loss events in an automobile insurance division. The data was

collected from a large Swiss insurance company between 2004 and 2011.

The target variable being dichotomous, we employ logistic regression

models to determine significant predictors of the presence of fraud in

claims. The fit and adequacy of the different models, and particularly

the final one, are assessed with the help of different measures. The anal-

ysis is rounded off with an in-depth examination of the effect of the loss

amount on the likelihood of engaging in fraudulent activities.

The results of our logistic regression analyses portray fraud-prone

policyholders as middle-aged individuals who prefer to drive high-valued

cars and having signed a leasing contract more often than their hon-

est counterparts. With regard to their driving behavior, individuals

engaging in fraudulent activities prove to be rather experienced and

safe drivers. They are characterized by having a low number of claims

throughout their entire insurance relationship. Particularly noteworthy

is the fact that they tend to file fraudulent claims for comparably small

loss amounts, probably with the intention of remaining undetected. In

a similar manner, they try to not attract attention by filing claims too

late after the insured loss event occurred.

4 Conclusion and Critical Discussion 115

Another central result of this study is the empirical documentation

of the link between loss amount and the probability of resulting fraud.

As previous research has already suggested, the magnitude of an insured

loss event has an inverse effect on the likelihood of taking fraudulent ac-

tivities into consideration. The main reason for this observation can be

policyholders’ anticipation of auditing strategies to remain undetected

and collect on the higher indemnification.

Our findings could be highly relevant to fraud investigators and un-

derwriters alike. The information regarding fraud indicators can be uti-

lized to perform auditing more effectively. Investigators would be given

the opportunity to focus specifically on those claims which are deemed

to have a high likelihood of being dishonest. Furthermore, the knowl-

edge that some individuals are more prone to inflating loss amounts than

others may be useful for other aspects of risk management as well. With

regard to the pricing of insurance policies, the information on whether

an individual should be counted among the fraud-prone or honest pol-

icyholders may be a relevant differentiation criterion. As part of the

risk selection process, insurance companies may even decide not to pro-

vide coverage for individuals who can be expected to defraud the com-

pany to a large extent or who are unwilling to pay the corresponding

insurance premium. These options are particularly interesting, since

limited resources will prevent investigation units from verifying all in-

coming claims, even those which exhibit sufficient signs of the presence

of fraud.

As with all studies, the current study has some limitations which may

establish a basis for future research. Relying on the insurance company’s

decision as to which incoming claims to audit and which to indemnify

right away, may have biased our view on potential fraud indicators. On

the one hand, determinants which are identified based on a preselected

sample predict the overall likelihood of fraud correctly. However, if they

were already among the company’s selection criteria, they may tend to

overestimate the actual probability of its occurrence being amenable to

the self-fulfilling prophecy. On the other hand, by disregarding part of


the dishonest cases due to omission error, we may have been unable to

capture additional fraud indicators, possibly even more suitable ones for

predicting the existence of fraud in a claim.

5 Appendix 117

5 Appendix

Variable Definition

Policyholder Characteristics

Policyholder Age Age of policyholder by the time of loss

occurrence

Citizenship Policyholder’s citizenship

(equals Swiss or other)

area of residence Policyholder’s area of residence withinSwitzerland (equals ge, fr or it)

Vehicle Characteristics

Vehicle age Vehicle age at the time of loss occurrence

vehicle type Type of vehicle

(equals car, transport or motorcycle)

Vehicle value Value of vehicle including accessories

(in CHF)

Leasing Vehicle is leased (equals 1, otherwise 0)

Policy Characteristics

no. consec. loss-free years Number of consecutive years without

filing a claim

no. previous records Total number of claims filed to date

bonus protection clause Policy includes a bonus protection clause

(equals 1, otherwise 0)

Loss Characteristics

Type of damage Type of damage indemnification is seekedfor

(equals theft, glas, collision or others)

loss amount Estimated loss amount of the claim

(in CHF)

delay in filing claim Time lag between occurrence of loss andfiling claim to insurance company in days

Table 11: Explanatory Variables Used in the ModelsAn overview of all variables and their respective definitions contained in our data set. Wedistinguish between variables on the policyholder, vehicle, policy and loss level. Based onthis information, we perform logistic regression to determine potential indicators for thepresence of fraud in a claim.


vif

Policyholder age 1.076

citizenship 1.058

area of residence 1.154

vehicle age 1.345

vehicle type 1.587

vehicle value 1.255

leasing 1.324

no. consecutive loss-free years 1.154

no. previous records 1.170

bonus protection clause 1.260

type of damage 1.513

loss amount 1.202

delay in filing claim 1.022

Table 12: Variance Inflation Factors for All Explanatory Variables Usedin the AnalysesThe variance inflation factors are employed to detect potential multicollinearity with re-gard to the explanatory variables. All corresponding values remaining below the criticalthreshold value - with 1.587 for the variable vehicle type being the maximum - this can beruled out.

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119

Filed Claims Audited Claims Not Audited Claims

mean s.d. mean s.d. mean s.d. p-value

N=1,429,896 N=7407 N=1,422,489

Policyholder age 44.89 14.99 39.18 13.87 44.92 14.99 < 0.0001

Vehicle age 6.21 5.12 7.39 5.75 6.21 5.12 < 0.0001

Vehicle Value (CHF) 44,948 38,076 48,313 59,250 44,931 37,934 < 0.0001

No. consec. loss-free years 3.45 2.16 4.26 2.33 3.44 2.15 < 0.0001

No. previous records 4.67 33.02 3.18 7.55 4.68 33.10 < 0.0001

Loss amount (CHF) 1,775 3,760 8,711 16,996 1,740 3,535 < 0.0001

Delay in filing claim (days) 19.17 40.23 15.90 43.61 19.19 40.21 < 0.0001

Table 13: Descriptive Statistics for the Whole Sample CompositionThis table reports the mean and standard deviation (s.d.) of different characteristics related to policyholder, vehicle, policy and loss withregard to the full sample of filed claims. This information is narrowed down particularly for the two subsamples of audited claims and notaudited claims. Furthermore, the last two columns provide the results of a two-sample t-test.

120

IIIEmpiricalAnalyses



Policyholder related characteristics

Citizenship

Swiss 1,055,362 73.98 4,363 58.90 1,050,999 74.06

other 371,131 26.02 3,044 41.10 368,087 25.94

Total 1,426,493 100 7,407 100 1,419,086 100

Area of residence

German-speaking part 1,001,286 70.38 5,313 72.09 995,973 70.37

French-speaking part 338,016 23.76 1,682 22.82 336,334 23.76

Italian-speaking part 83,340 5.86 375 5.09 82,965 5.86

Total 1,422,642 100 7370 100 1,415,272 100

Vehicle related characteristics

Vehicle type

Car 980,258 92.24 3,525 71.34 976,733 92.33

Transport 52,930 4.98 262 5.30 52,668 4.98

Motorcycle 29,588 2.78 1,154 23.36 28,434 2.69

Total 1,062,776 100 4,941 100 1,057,835 100

Leasing

Leased 340,247 23.80 1,404 18.96 338,843 23.82

Not leased 1,089,649 76.20 6,003 81.04 1,083,646 76.18

Total 1,429,896 100.00 7,407 100.00 1,422,489 100.00

Table 14: Descriptive Statistics for the Whole Sample CompositionThis table describes the sample composition using different categorical variables on the policyholder, vehicle, policy and loss level.In addition, the information is further differentiated with regard to audited and not audited claims.

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Policy related characteristics

Bonus protection clause

Included 746,440 52.20 2,991 40.38 743,449 52.26

Not included 683,456 47.80 4,416 59.62 679,040 47.74

Total 1,429,896 100.00 7,407 100.00 1,422,489 100.00

Loss related characteristics

Type of damage

Theft 9,049 0.63 2,437 32.90 6,612 0.47

Glass 367,832 25.77 1,130 15.26 366,702 25.83

Collision 328,867 23.04 1,368 18.47 327,499 23.07

Others 721,376 50.55 2,472 33.37 718,904 50.64

Total 1,427,124 100.00 7,407 100.00 1,419,717 100.00

Table 14: Descriptive Statistics for the Whole Sample Composition – continued


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127

Part IV

What Drives Insurers’

Demand for Cat Bond

Investments? Evidence from a

Pan-European Survey

Abstract

Despite the fact that insurance and reinsurance companies should be

familiar with the risk characteristics of the cat bond asset class, they

jointly account for less than 10 percent of the current investor demand

in the market. In order to be able to develop explanations for this ob-

servation, a deeper insight into the respective decision-making process

is needed. Accordingly, our main research goal in this paper is to iden-

tify major determinants of the cat bond investment decision of insurers.

For this purpose, we conducted a comprehensive survey among senior

executives in the European insurance industry. Evaluating the corre-

sponding data set by means of exploratory factor analysis and logistic

regression methodology, we are able to show that the firm’s expertise and

experience with regard to cat bond investments, the perceived fit of the

asset class with its asset and liability management philosophy, as well

as the prevailing regulatory regime are significant drivers of an insurer’s

propensity to invest. These statistical findings are supported by further

qualitative survey results and additional information from structured in-

terviews with the investment managers of four large dedicated cat bond

funds.16

16A. Braun, K. Muller, and H. Schmeiser. What Drives Insurers’ Demand for CatBond Investments? Evidence from a Pan-European Survey. Working Papers on Risk

Management and Insurance, 2012.This paper has been accepted for publication at The Geneva Papers on Risk and

Insurance.

128 IV Empirical Analyses

1 Introduction

For almost two decades, insurance and reinsurance companies have been

employing insurance-linked securities (ILS) and derivatives to hedge a-

gainst peak losses in the capital markets. The undoubtedly most suc-

cessful of these alternative risk transfer measures is the catastrophe (cat)

bond, an instrument that allows natural disaster risk to be traded over

the counter. As is typical for securitizations, cat bonds are issued out of a

special purpose vehicle (SPV), which then holds the principal paid by in-

vestors in the form of highly rated collateral.17 The sponsoring company

enters into a reinsurance contract (or cat swap) with the SPV and, in

case a catastrophe occurs and causes losses in excess of the preset thresh-

old, it is reimbursed with the proceeds of the collateral while investors

lose all or part of their principal. To determine whether a payment un-

der the embedded reinsurance contract is due, cat bond structures can

feature a variety of different trigger mechanisms.18 Up until the trig-

ger event or maturity, investors are compensated for bearing the natural

disaster risk through regular coupons that typically consist of a float-

ing interest rate such as LIBOR, plus a risk-adjusted spread (see, e.g.,

Braun, 2012). Due to their comparatively high yields and rather low cor-

relations with traditional asset classes, cat bonds have repeatedly been

described as an appealing investment opportunity (see, e.g., Litzenberger

and Beaglehole, 1996, Schoechlin, 2002, Cummins and Weiss, 2009). Yet,

the current investor base for this kind of asset is largely dominated by

money managers and a few specialized investment funds (see, e.g., Swiss

Re, 2009). This raises questions about the determinants of the institu-

tional demand for cat bonds and, in turn, limits to the future growth

potential of this still relatively small segment of the capital markets. A

particularly puzzling phenomenon in this context is the fact that these

17Note that until early 2009, cat bonds used to be protected against collateral lossesby means of a total return swap (TRS). However, in the aftermath of the financial cri-sis four transactions ended up in distress, since the default of their swap counterpartyLehman Brothers coincided with a severe impairment of the collateral assets. Con-sequently, the TRS feature has been removed in more recent transactions. Instead,credit risk is meant to be largely eliminated through stricter collateral arrangements(see, e.g., Towers Watson, 2010).

18A description of the different trigger types for cat bonds can, e.g., be found inSwiss Re (2006).

1 Introduction 129

instruments seem to play a negligible role in the asset management of

insurance companies, which, in contrast to other institutional investors,

such as banks and pension funds, should be very familiar with the inher-

ent risks.

Several authors have discussed potential catalysts and impediments

for the evolution of the catastrophe risk markets, considering both tradi-

tional reinsurance and securitization. Froot (1999), for example, suggests

that securitization can help to improve the efficiency of the distribution

of natural hazard losses, and postulates five key success factors for cat

bond issues. Furthermore, Niehaus (2002) explores market imperfections

that hamper the optimal sharing of natural disaster risk via reinsurance

contracts and cat bonds. In his opinion, the unresolved question of pric-

ing these instruments in a portfolio context has a very important impact

on the demand, since it determines whether or not investors believe that

the asset class truly exhibits zero-beta characteristics. Similarly, Froot

(2001) develops a number of supply-and-demand-related explanations

for the fact that the empirically observed amount of reinsurance and cat

bond transactions is considerably lower than suggested by risk manage-

ment theory. He finds the market power of reinsurance companies and

impediments to the inflow of financing from the capital markets to be

the most likely reasons for this phenomenon. Another related paper has

been written by Gibson et al. (2007), who examine why capital-market-

based risk transfer solutions have failed to replace traditional reinsurance

as the primary means for sharing catastrophe risk. They conclude that

reinsurance should be preferred in situations where information from the

capital markets is costly to acquire and largely redundant. In addition,

Cummins and Trainar (2009) consider the advantages and disadvantages

of reinsurance and securitization from a risk management perspective. In

this context, they note that cat bonds primarily attract investors due to

their still relatively high yields, their low correlation with traditional as-

set classes, the fact that they are collateralized, and the lower complexity

as well as better alignment of interest between investors and ceding com-

panies compared to other types of asset-backed securities (ABS). Apart

from that, Ibragimov et al. (2009) derive a model that serves to ex-


plain the limited supply of protection against catastrophe risk offered

by insurers and reinsurers. In their view, the typical heavy-tailed loss

distributions associated with natural disasters imply a substantial re-

duction in diversification benefits that may lead to a situation where

individual firms do not have an incentive to offer coverage. Finally, Lak-

dawalla and Zanjani (2011) illustrate that the full collateralization of cat

bonds hinders deeper market penetration, since diversification benefits

in the context of traditional reinsurance portfolios allow for a more effi-

cient deployment of capital. In their view, this impediment can only be

surpassed if securitizations offer substantially lower friction costs than

reinsurance contracts.

Another strand of related literature is directly concerned with factors

that determine the supply of cat bonds by sponsors and the demand for

these instruments by investors. Bantwal and Kunreuther (2000) employ

behavioral economic aspects such as ambiguity aversion, myopic loss

aversion, and the fixed costs of education in order to explain institu-

tional asset managers’ reluctance to invest in cat bonds. They suggest

that, to increase demand and promote further market growth, issuers

should aim for a larger degree of security standardization, reduce pric-

ing uncertainty, and strive to enhance investor expertise with regard to

the asset class. Moreover, within his comprehensive overview of alterna-

tive risk transfer instruments, Cummins (2005) describes cat bonds as a

valuable means of portfolio diversification for investors, and emphasizes

that more standardized and transparent transactions as well as the de-

velopment of a public secondary market would help to realize the full

potential of the asset class. Cummins (2008) additionally mentions the

difficulty involved in obtaining transactional information as an obstacle

for further growth. A wide range of issues that hinder the expansion

of the ILS markets is also discussed in a study by the World Economic

Forum (2008). Amongst others, the considered problems for sponsors

comprise basis risk, the instruments’ accounting and regulatory treat-

ment, inconsistent rating methodologies, insufficient data quality and

disclosure, the costs of structuring a securitization deal, and the rela-

tively low level of experience with securitization in the insurance indus-

1 Introduction 131

try. Investors, on the contrary, are said to be concerned about the lack

of standardization, the limited liquidity and secondary market trading

activity, the nontransparent nature of certain trigger mechanisms, and

the complexity involved in ILS valuation. Similar issues are identified by

Cummins and Weiss (2009) as well as Bouriaux and MacMinn (2009),

who also discuss major demand drivers, such as the risk-return profile

and diversification benefits of the asset class and the latest advances in

risk modeling methodology. Barrieu and Louberge (2009), in contrast,

claim that the common arguments for the supposedly disappointing de-

velopment of the cat bond market to date, such as the lack of investor

familiarity with the instrument, parameter uncertainty, and the trade-off

between moral hazard and basis risk, are not convincing. Instead, they

suspect downside risk aversion in combination with ambiguity surround-

ing the correlation between natural disaster losses and capital market

crash scenarios to be responsible for the limited demand. Finally, Ha-

gendorff et al. (2011) draw on the model framework proposed by Merton

(1974), in order to demonstrate that the risk reduction benefits of cat

bonds are confined to sponsors with a high default probability or a large

exposure to natural disaster risk. They point to this lack of universal

applicability as an explanation for the underwhelming development of

the market to date.

Despite the relatively large body of literature on supply, demand,

and growth drivers in the markets for catastrophe risk, to the best of our

knowledge, relatively little is known about the motivation of insurance

companies to act as cat bond investors. In particular, no analysis of the

determinants of their respective investment decision has been conducted

to date. Therefore, with this paper we aim to address an important re-

search gap by identifying and analyzing the main drivers and obstacles

regarding the demand for cat bond investments in the insurance industry.

For this purpose, we developed a comprehensive questionnaire that has

been distributed to senior executives of almost 500 European insurance

companies. Moreover, to complement the statistical data and qualita-

tive information provided by the survey participants and provide addi-

tional evidence for the robustness of our results, we have also conducted


structured interviews with the investment managers of the four largest

dedicated cat bond funds that together absorb almost 80 percent of the

outstanding volume. Our findings should provide a thorough insight into

the decision-making process that underlies cat bond investments of in-

surance companies and can thus help to address pressing issues, reduce

investment barriers, and support further growth of the cat bond market.

The remainder of this paper is structured as follows. In Section 2,

we provide facts on the current size and investor base of the cat bond

market and develop eight hypotheses concerning the determinants of an

insurance company’s decision to invest in this asset class. Furthermore,

Section 3 contains a description of our survey as well as a brief introduc-

tion to the statistical techniques of exploratory factor analysis and logis-

tic regression that are used to evaluate the resulting data set. Section 4

represents the main part of the paper, including descriptive statistics,

the derivation of our key empirical findings, and the discussion of the

qualitative results from the open survey questions and expert interviews.

Finally, in Section 5 we draw our conclusion and propose ways to tackle

the major barriers that currently seem to prevent insurance companies

from engaging in cat bond investments on a larger scale.

2 The Demand for Cat Bonds

2.1 Current Market Size and Investor Base

Although, in its early days, the cat bond market suffered from low ca-

pacities and a lack of investor interest, it has undergone a major devel-

opment since the beginning of the 1990s. In the 10 years between 1997

and 2007, issuance volume has increased more than sevenfold from less

than USD 1 billion to over USD 7 billion (see Cummins and Weiss, 2009).

Furthermore, Guy Carpenter (2011) estimates that the outstanding risk

capital for nonlife cat bonds summed up to more than USD 10 billion in

2011. Apart from the market size, a significant evolution could also be

observed in the investor base of this asset class. According to Swiss Re

(2009), primary insurers and reinsurers together purchased a total of 55


percent of the cat bond volume issued in 1999. The remaining demand

came from money managers (30 percent) as well as hedge funds, banks,

and dedicated cat bond funds (5 percent each). By 2009, however, the

market structure had changed dramatically, with dedicated cat bond

funds (46 percent), money managers (23 percent), and hedge funds (14

percent) now providing the vast majority of risk capital. At the same

time, the combined share of insurance and reinsurance companies had

fallen to a mere 8 percent. To explain this low level of demand compared

to other types of institutional investors, the driving factors behind the

investment decision of asset managers in the insurance sector need to be

revealed.

2.2 Development of Hypotheses

In the following, we develop a total of eight hypotheses that served us

as guidance with regard to the design of the questionnaire as well as

the schedule for the expert interviews. Although some of the postulated

determinants have already been mentioned in earlier articles, they have

not yet been empirically tested with an explicit focus on insurance com-

panies as investors.

Larger insurers generally have more financial and professional re-

sources at their disposal than small or medium-sized companies. Conse-

quently, they may, for example, afford to put the necessary cat-modeling

and data evaluation technology in place, hire additional asset manage-

ment specialists, or establish a dedicated investment team that focuses

on the analysis of ILS. This implies that the sheer size of an insurance

company could have an influence on its ability to gain access to the cat

bond market, leading us to hypothesize the following:

H1: Larger insurance companies are more likely to invest in

cat bonds.

In addition, due to the ever-growing importance of modern risk man-

agement techniques and processes, insurers make their investment deci-

sions in accordance with preset strategic asset and liability management


(ALM) goals. Thus, they will tend to avoid assets that are perceived to

be at odds with their ALM philosophy, while focusing on investments

that they find to be overall attractive and to fit well into the firm’s

portfolio. We therefore state the following hypothesis:

H2: The better the perceived fit of cat bonds with the strategic

ALM goals of an insurer, the more likely the company is to

invest.

Asset managers in the insurance industry continuously search for

and analyze potential investment opportunities. Due to the complexity

of today’s capital markets, organizations need to exhibit a lot of in-

house expertise and experience if they want to be able to structure and

maintain portfolios of a wide range of assets. In particular, with respect

to niche markets such as cat bonds, an experienced and well-attuned

asset management is a crucial factor for investment success. Based on

these considerations, we postulate:

H3: More expertise and experience with regard to the cat bond

asset class increase an insurer’s propensity to invest.

It has been repeatedly emphasized that cat bonds exhibit an attrac-

tive risk-return profile. However, potential investors need to perceive

and value this benefit as such, in order to become interested in the asset

class. Hence, we hypothesize:

H4: Insurance companies that perceive the risk-return poten-

tial of cat bonds to be attractive are more likely to invest.

Another typical characteristic of cat bonds is their low correlation

with other asset classes. This circumstance provides them with a consid-

erable diversification potential. For this particular benefit to play a role

with regard to the investment decision, however, the firms need to notice

and acknowledge it. This observation leads to the following hypothesis:

H5: The propensity of insurers to invest in cat bonds rises

with the degree to which they perceive the asset class’s diver-

sification potential.


Furthermore, it can be expected that insurers are more likely to con-

sider investments in cat bonds if they perceive them as rather liquid and

standardized assets, which are associated with low administration costs.

We summarize these and similar aspects in a factor called perceived ad-

ministrative complexity and hypothesize the following:

H6: The less administrative complexity insurance companies

associate with cat bonds, the more likely they are to invest in

this asset class.

Whether an asset class represents an adequate investment choice gen-

erally depends on the evaluation of data and information. The decision-

making process of insurance companies can be facilitated if, for example,

transaction data, pricing information, and historical performance figures

for the respective asset classes are readily available. Hence, we derive

the following hypothesis:

H7: The more they perceive relevant data and information

on the asset class to be readily available, the more likely in-

surance companies are to invest in cat bonds.

For the protection of the policyholders’ interests, the assets of an

insurance company are classified as either tied (restricted) or free. The

free assets reflect the firm’s equity capital and thus typically account for

a comparatively small percentage of the total portfolio. A much larger

fraction, in contrast, is represented by the tied assets, which are meant

to cover the firm’s technical provisions at all times. Consequently, they

need to adhere to strict requirements with regard to investment types,

diversification, and risk management.

As will be discussed in Section 4, all companies in our sample are ei-

ther subject to EU or Swiss regulation. Explicit lists of asset categories

that can be employed to cover the technical provisions of insurers within

the European Union are included in Article 21 of the third nonlife in-

surance Directive of the European Council (Directive 92/49/EEC) and

Article 23 of the Directive of the European Parliament and the Council


concerning life assurance (Directive 2002/83/EC). These legal acts com-

prise a general category termed “debt securities, bonds, and other money

and capital market instruments”, which, taking into account their fixed

income format, also seems applicable to cat bonds. However, in accor-

dance with this EU legislation, individual member states may also estab-

lish more detailed guidelines with regard to the characteristics of accept-

able investments. In Germany and Austria, for example, the act on the

supervision of insurance undertakings (in German: “Versicherungsauf-

sichtsgesetz”, VAG) empowers the government and the national regu-

latory authority, respectively, to enact provisions that contain binding

conditions for the tied assets.19 These legal acts, called “Anlageverord-

nung” (AnlV) in Germany and “Kapitalanlageverordnung” (KAVO) in

Austria, do not explicitly rule out cat bond investments. In addition,

they contain an opening clause for asset classes that are not included in

their predefined lists.20 Since the requirements with regard to the tied as-

sets in other European countries are also based on the above-mentioned

EU directives, they can be assumed to be quite similar. Hence, we do

not expect explicit regulatory constraints with regard to the cat bond

asset class for insurance companies in EU member states.

Furthermore, in Switzerland the act on the supervision of insurance

undertakings states that the Swiss Federal Council may enact provisions

that govern tied assets and leave it up to the Swiss Financial Market Su-

pervisory Authority (FINMA) to determine additional details.21 The re-

spective guidelines have been incorporated into Article 79(1) of the “Auf-

sichtsverordnung” (AVO) and are further substantiated in FINMA’s cir-

cular letter on the investment of tied assets (see FINMA, 2008). Clause

II.D.a of this document, which includes the general principles with regard

to eligible investments, states that the tied assets must not include in-

surance risk, and clause III.C.b.bb explicitly forbids the purchase of ILS.

Hence, Swiss insurers may only consider cat bond investments within

their free assets. This implies that their asset management departments

19See paragraph 54(2) VAG Germany and paragraph 78(3) VAG Austria.20These opening clauses can be found in paragraph 2(2) AnlV and paragraph 2(1)

No. 9 KAVO.21See Article 20 VAG Switzerland.

3 Data and Methodology 137

have less options to employ the instrument than those of their European

counterparts. The consideration of this legal background results in our

last hypothesis:

H8: Due to binding regulatory constraints, Swiss insurers are

less likely to invest in cat bonds.

In this context it should be noted that regulatory constraints in the

broader sense could also arise due to the capital requirements associated

with cat bond investments under the Swiss Solvency Test (SST) or Sol-

vency II. More specifically, if an insurer perceives the resulting capital

charges to be ambiguous or inappropriate, it could tend to avoid the asset

class. However, under both regulatory frameworks cat bond investments

are virtually treated in the same way as the catastrophe risk exposure

incurred through traditional (re)insurance contracts. Hence, we do not

expect a significant impact on the investment decision of insurance com-

panies and refrain from formulating an explicit hypothesis. Similarly, we

deem it unlikely that the accounting treatment of the instrument turns

out to be relevant in this regard. Nevertheless, our survey included a

set of questions to measure the firm’s perception of the capital require-

ments and accounting treatment of cat bond investments. Based on the

corresponding information, the correctness of these expectations will be

confirmed.

3 Data and Methodology

3.1 Development of Measures

Before the development of our questionnaire, we conducted several in-

terviews with ILS experts from a Swiss reinsurance company. The aim

was to identify and better understand potential factors driving the de-

mand for cat bond investments. Based on the results, we then devised

measures and scales for the determinants and generated an initial set of

items.22 After having prepared a first draft of the questionnaire, we again

22To the best of our knowledge, there are no existing scales in the literature thatwould fit the context of our study.


consulted industry professionals and risk management academics to ob-

tain in-depth feedback concerning wording and completeness, based on

which we implemented final changes by rephrasing, including, or deleting

certain items.

3.2 Participant Recruitment

To recruit relevant participants for our web-based survey, we made use of

the key informant technique. The aim was to contact senior executives,

preferably CEOs and CFOs, since they should be well informed about the

companies’ strategic investment decisions as well as the corresponding

reasons behind them. Hence, we collected the addresses of a total of 490

insurance and reinsurance companies from Austria, France, Germany,

Italy, the Netherlands, Sweden, Switzerland, the UK, Finland, Portugal,

Belgium, and Greece. Based on the gathered information, we invited

the senior executives per regular mail to take part in our survey. In

a first stage, the questionnaire was available online for three weeks in

February 2012. Subsequently, two reminders were sent out per e-mail to

those persons whose e-mail addresses were available. This happened at

an interval of two to three weeks so that the companies had a total of

nine weeks’ time to answer the questionnaire. While survey participation

in general was anonymous, the respondents were offered to be sent the

results of our study if they chose to include their contact information.

3.3 Sample Characteristics and Imputation

Overall, 64 companies reacted to the invitation, which corresponds to a

response rate of 13.1 percent. On average, it took the participants 11

minutes to complete the survey. However, a number of firms terminated

the questionnaire too early to be included in our analysis. We therefore

had to adequately impute missing values as far as possible or remove all

cases for which essential items were missing and imputation was impos-

sible. Our final data set is based on the responses of 44 participants,

who completed the essential parts of the questionnaire, such as the com-

pany background, and indicated whether or not they have invested in

3.4 Exploratory Factor Analysis 139

cat bonds in the past and/or plan to do so in the future.23 Of these 44

participants, 36 provided their views on the potential determinants that

have an impact on the investment decision. This subsample will be used

for the inference statistical analysis.

3.4 Exploratory Factor Analysis

Apart from the company size and constraints due to the regulatory

regime, the potential determinants of the cat bond investment decision

hypothesized in Section 2.2 are likely to be latent variables, i.e., multi-

faceted constructs that are not directly observable. In order to capture

those, we have included a total of 41 items (observed variables) in the

questionnaire, which were measured on six-point Likert scales.24 Poten-

tial biases due to individuals who are too inexperienced with the subject

to provide a reliable opinion are minimized, since we additionally al-

lowed the respondents to choose a “do not know” button for each item.

The derivation of the data points for each potential determinant will be

conducted by means of exploratory factor analysis (EFA), a statistical

methodology that explains the covariance (correlation) structure of ob-

served random variables in terms of a smaller number of latent variables.

The following is an analytical representation of the general EFA model:25

X = Λξ + δ, (58)

where X is the vector of observed variables (items), Λ represents the

factor loadings matrix, ξ is the vector of latent variables (factors), and

23Fourteen of the participants provided us with information about their positions inthe company. According to their statements, five Chief Investments Officers and twoother members of the executive boards answered our questionnaire. Furthermore, twosurvey participants are directors whereas another five claimed they were appointedeither Head of Asset Management or Senior Risk Manager. Thus, we believe that weactually did approach the key informants we wanted to.

24Likert scales are a common way to capture an individual’s level of agreement ordisagreement with a specific statement (see Likert, 1932). An even number of pointsmeans that a neutral answer is not possible. Instead, the respondent is forced tochoose a positive or negative stance.

25The notations in this subsection have been adopted from Joreskog (1967).


δ stands for the vector of unique factors (residuals). Applying matrix

algebra, one can derive the covariance matrix Σ implied by the model:

Σ = ΛΦΛ′ + Ψδ, (59)

with Φ being the covariance matrix of the factors and Ψδ being the co-

variance matrix of the residuals. The parameters (factor loadings and

residual variances) for the EFA model are determined by means of maxi-

mum likelihood estimation (MLE), so that the model-implied covariance

(correlation) matrix fits its empirically observed counterpart as closely

as possible.26 Based on the derived factor loadings, it is possible to

compute factor score estimates ξ. For this purpose, we will choose the

regression method, which employs the sample covariance matrix Σ and

the estimated factor loadings matrix Λ as follows:

ξ = Λ′Σ−1X. (60)

These factor scores can then be used as a measure for the hypothe-

sized latent determinants of the cat bond investment decision in further

analyses.

3.5 Logistic Regression Model

To address our research question, we require a statistical methodology

that determines the influence of a set of metric explanatory variables

xi on a binary (dichotomous) dependent variable y, i.e., one that takes

on only two values: one and zero (investor and non-investor). In this

situation, linear regression is unsuitable, since it may also produce out-

comes of less than zero and greater than one, and its basic assumptions

of homoscedastic and normally distributed residuals are violated (see

Wooldridge, 2008). Given these drawbacks of the linear approach, we

decide to resort to a binary response model to predict the probability

that the dependent variable y assumes a value of one, given the realiza-

tions of a number of independent variables xi (i = 1...n). More specifi-

26Note that the standard EFA model requires the observed variables to be normallydistributed.

3.5 Logistic Regression Model 141

cally, we employ the common logit model, which is based on the logistic

function:27

p(z) =1

1 + exp(−z).28 (61)

The logistic function translates any real number z into a value p(z)

between zero and one.29 In order to derive the logistic regression model,

z is assumed to be a latent variable called the logit that can be expressed

as a linear combination of the regressors xi (i = 1...n):

z = β0 + X’β + ǫ = β0 + β1x1 + β2x2 + ... + βnxn + ǫ, (62)

where β0 denotes the intercept, the βi are the regression (logit) coeffi-

cients, and the error term ǫ is assumed to be independent of the xi.30

The logit equals the natural logarithm of a magnitude termed the odds

ratio (OR), which equals the probability of the dependent variable tak-

ing on the value one divided by the probability of it taking on the value

zero:

OR =p(y = 1|X)

p(y = 0|X)= exp(β0 + β1x1 + β2x2 + ... + βnxn + ǫ). (63)

Being defined on [0,+∞), OR is the key measure of effect strength

in the logistic regression model. If it equals one, both outcomes of the

dependent variable are equally likely. The further it deviates from one,

the stronger the (positive or negative) link between the dependent vari-

able and the regressors.

27The following derivation of the logit model is based on Wooldridge (2008).28This expression also represents the cumulative distribution function for a logisti-

cally distributed random variable.29In contrast to logistic regression, discriminant analysis, which is another binary

response model, also generates values above one and below zero. Apart from that itrequires the explanatory variables to be normally distributed (see Press and Wilson,1978). Therefore, it is not considered in the context of our analysis.

30In matrix notation, X’ is the random vector of explanatory variables and β

represents the vector of regression coefficients.


Combining Equations (61) and (62), the relationship between the

explanatory variables xi and the response probability p(y = 1|X) can be

expressed as follows:31

p(y = 1|X) = 1/(1 + exp(−β0 − β1x1 − β2x2 − ...− βnxn − ǫ)). (64)

Hence, although the observed values of the dependent variable are

binary, the logit model actually describes a continuous variable, i.e., the

probability of y assuming a value of one. The βi are determined by means

of MLE. More specifically, based on the data for y and the explanatory

variables xi, an iterative procedure serves to choose the logit coefficients

that are most likely associated with the observed values.

4 Empirical Results

4.1 Descriptive Statistics

In this section, we present descriptive statistics to characterize the com-

position of our sample. The first column of Table 15 shows the number

(and percentages) of insurance companies categorized by country, busi-

ness model (insurer, reinsurer), business line (life, nonlife, multiline), and

geographic investment scope (global, regional). In addition, we indicate

whether or not the firms act as cat bond sponsors, invest in securitiza-

tions in general, and belong to a larger insurance group. Accounting for

31.82 percent of the survey respondents, Swiss insurers are slightly over-

weighted in the data set. Apart from that, however, the participants are

relatively evenly spread across European countries. Furthermore, almost

80 percent of the covered firms are primary insurers. This is a positive in-

dication for the representativeness of the sample, since reinsurers are also

much rarer in the reference population (i.e., European insurance compa-

nies). Similarly, a majority of about 70 percent run a multiline insurance

business, comprising both life and nonlife divisions.32 With respect to

31Note that z, OR, and p(y = 1|X) essentially provide the same information. Aprobability of 0.5 corresponds to a logit of 0 and an OR of 1. Each of these valuesimplies that both outcomes of y exhibit the same likelihood.

32Four of the firms in this category responded that they additionally run a healthinsurance line.


their geographic investment scope, around 60 percent replied that they

exclusively focus on regional (national or European) assets and markets,

while only 40 percent consider themselves to be global investors. Hence,

we seem to have a well-balanced mix of small, medium-sized, and large

companies. Moreover, more than 80 percent of the respondents stated

that they do not act as cat bond sponsors. Again, this implies that the

data should be representative, since only a few large primary insurers

and reinsurers in Europe with the resources and capabilities to spon-

sor and structure cat bond transactions have actually employed this risk

transfer instrument to date. Finally, half of the firms in the sample invest

in at least one other type of securitization, such as ABS, collateralized

debt obligations (CDOs), or covered bonds, and the vast majority of the

responding entities are part of a group.

In the second and third column of Table 15, we have split the sample

into those firms that do and those that do not invest in cat bonds.33 As

could be expected, only about 30 percent (13/44) of the respondent firms

actually invest in cat bonds. Taking into account the low percentage of

insurers among the current investor base of the cat bond asset class

as discussed in Section 2.1, the large fraction of 70.45 percent (31/44)

non-investors is another cue for the representativeness of our sample. In-

terestingly, the majority of investors (61.54 percent) come from Austria,

Germany, or Italy. At least half of the survey participants from these

countries have disclosed themselves as cat bond investors. Furthermore,

most non-investors in the sample are based in Switzerland (38.71 per-

cent), and over 90 percent of the non-investors are primary insurers. In

contrast, more than 40 percent of the investors are reinsurers or, to put

it differently, two-thirds (6/9) of the reinsurers in the sample do invest in

cat bonds. This might be some initial evidence for hypotheses 1, 2, and

3, since the firm’s size, the expertise and experience with cat bonds, as

well as the fit of the asset class with the firm’s strategic ALM are charac-

teristics that can be expected to vary considerably between the average

primary insurer and reinsurer. Similarly, the fact that almost all non-

33We define cat bond investors as those insurance companies, which stated thatthey will continue or begin to hold cat bonds in their asset portfolios in the future.


Full Sample Investors Non-investors


Austria 4 9.09 2 15.38 2 6.45

France 1 2.27 0 0.00 1 3.23

Germany 6 13.64 3 23.08 3 9.68

Italy 5 11.36 3 23.08 2 6.45

Netherlands 2 4.55 0 0.00 2 6.45

Sweden 3 6.82 1 7.69 2 6.45

Switzerland 14 31.82 2 15.38 12 38.71

UK 2 4.55 1 7.69 1 3.23

Finland 3 6.82 1 7.69 2 6.45

Portugal 2 4.55 0 0.00 2 6.45

Belgium 1 2.27 0 0.00 1 3.23

Greece 1 2.27 0 0.00 1 3.23

Total 44 100.00 13 100.00 31 100.00

Primary Insurers 35 79.55 7 53.85 28 90.32

Reinsurers 9 20.45 6 46.15 3 9.68

Total 44 100.00 13 100.00 31 100.00

Life Business 4 9.09 1 7.69 3 9.68

Nonlife Business 9 20.45 4 30.77 5 16.13

Multiline Business 31 70.45 8 61.54 23 74.19

Total 44 100.00 13 100.00 31 100.00

Global Investor 18 40.91 7 53.85 11 35.48

Regional Investor 26 59.09 6 46.15 20 64.52

Total 44 100.00 13 100.00 31 100.00

Cat Bond Sponsor 7 15.91 6 46.15 1 3.23

No Cat Bond Sponsor 37 84.09 7 53.85 30 96.77

Total 44 100.00 13 100.00 31 100.00

Securitization Investor 20 45.45 11 84.62 9 29.03

No Securitization Investor 24 54.55 2 15.38 22 70.97

Total 44 100.00 13 100.00 31 100.00

Group 35 79.55 9 69.23 26 83.87

Single Entity 9 20.45 4 30.77 5 16.13

Total 44 100.00 13 100.00 31 100.00

Table 15: Sample CompositionThis table shows the composition of the sample of 44 firms that has been generated fromthe respondents of a survey among 490 European insurers and reinsurers. The data is cate-gorized by country, business model, business line, geographic investment scope, sponsoringactivity, other securitization investments as well as organizational structure. In addition,each category is further differentiated into cat bond investors and non-investors.


investors (96.77 percent) do not act as cat bond sponsors and a majority

of them have a regional investment focus (64.52 percent) supports these

hypotheses. The reason for this is that only a few large and experienced

reinsurance companies dominate the cat bond sponsoring business, and

insurers with a geographically limited asset management scope are likely

to be smaller and less experienced with rather exotic asset classes such

as cat bonds. In addition, judging by the higher share of pure nonlife

insurers among the investors, it seems that the propensity to purchase

cat bonds might somehow be related to the risk expertise that an insur-

ance company accumulates through its business lines. Lastly, we observe

that almost 85 percent of the cat bond investors in our sample also hold

other securitizations, while more than 70 percent of the non-investors

do not. Thus, the experience with and the general affinity to invest in

securitized assets could also exert an influence on insurance companies’

demand for cat bonds.

Table 16 contains mean, median, standard deviation, minimum, and

maximum for the number of employees, the balance sheet size, and the

premium volume of the firms in our sample. These variables have been

included in the survey as proxies for the company size. Again, we ad-

ditionally distinguish between investors and non-investors. When exam-

ining the respective figures, we notice that for all three variables the

medians are smaller than the means, i.e., the distributions seem to ex-

hibit some degree of positive skewness (long right tail). Moreover, the

minimum and maximum values indicate that the sample covers a range

of very differently sized companies. The smallest insurer, for example,

employs only 14 staff members, while the largest workforce amounts to

60,000 people.34 Similar observations can be made for the balance sheet

sizes and premium volumes. A simple comparison of the sample means

of these three size proxies between investors and non-investors reveals

that, on average, the former are larger. However, since this discrep-

ancy could be simply caused by the random draw through our survey,

one needs to rely on statistical inference in order to make a statement

about the underlying population of European insurance companies. The

34Note that all entities with less than 4,000 employees are part of insurance groups.


most common procedure in this regard is the two-sample t-test for the

equality of means. The typical prerequisites for this test are normally

distributed data, equal sample sizes, and equal sample variances (see,

e.g., Sawilowsky and Blair, 1992). The former condition can be checked

by means of the Kolmogorov-Smirnov (K-S) goodness-of-fit test, the re-

sults of which are displayed in the last two columns of Table 16. Since

we reject the null hypothesis of normality in all cases but one (see p-

values), the aforementioned two-sample t-test will not be applied. In-

stead, we decide to conduct the more robust Mann-Whitney U test to

assess whether the differences in the means between investors and non-

investors are statistically significant. This nonparametric test is based

on the null hypothesis that the two samples under consideration have

been drawn from the same distribution. The results are shown in Ta-

ble 17. For all three size proxies (number of employees, balance sheet

size, premium volume) the p-values exceed 0.1. To put it differently, this

is a first indication that company size might not matter with regard to

the cat bond investment decision of insurance companies.

Finally, to get an initial impression of the importance of some poten-

tial determinants discussed in Section 2.2, we have asked the insurance

companies that participated in the survey to state whether or not cer-

tain factors had an influence on their cat bond investment decision.35

Table 18 shows the respective results.36

Interestingly, the aspects expertise and experience, risk-return (and

correlation) profile, administrative complexity, and data availability are

considered relevant by the majority of investors, while they do not seem

to be of importance to most non-investors. Constraints due to capital

35As explained in Section 3.4, most of the determinants are latent factors, whichhave been measured by means of observed variables or so-called items. Within thequestionnaire, each determinant was represented by a whole battery of such items.The relevant/irrelevant questions to which we refer in this paragraph preceded thoseitem batteries. The only exception is the factor “perceived fit with the company’sstrategic ALM” (hypothesis 2), for which a relevance/irrelevance question has notbeen posed. The reason is that the respective item battery was included in a moregeneral section of the questionnaire that captured further details with regard to thefirm’s past, present, and future cat bond investments.

36Note that the number of respondents N has dropped from 44 to 36, since eightfirms have not provided information with regard to the item batteries for the latentvariables at all. Hence, imputation was not possible and the respective cases havebeen excluded from the following analyses due to missing data.

4.1

Descrip

tive

Statistics

147

Full Sample Mean Median S. D. Min Max K-S Stat. p-value

No. of Employees 6,667.80 1,225.00 13,365.14 14.00 60,000.00 0.3224 0.0002 ***

Balance Sheet (mn EUR) 38,975.24 10,492.93 78,202.53 0.18 400,000.00 0.3249 0.0002 ***

Premium Volume (mn EUR) 8,529.05 1,775.00 18,971.43 0.11 107,900.00 0.3265 0.0002 ***

Investors

No. of Employees 9,102.85 1,250.00 17,035.41 87.00 47,000.00 0.3644 0.0633 *

Balance Sheet (mn EUR) 50,347.32 22,500.00 84,651.67 360.00 240,000.00 0.3732 0.0392 **

Premium Volume (mn EUR) 8,580.91 3,735.00 11,197.83 460.00 32,600.00 0.2774 0.2697

Non-investors

No. of Employees 5,646.65 1,200.00 11,674.88 14.00 60,000.00 0.3147 0.0043 ***

Balance Sheet (mn EUR) 34,206.30 9,296.00 76,287.88 0.18 400,000.00 0.3334 0.0020 ***

Premium Volume (mn EUR) 8,507.31 1,308.00 21,580.55 0.11 107,900.00 0.3766 0.0002 ***

Table 16: Descriptive Statistics for the Company SizesThis table contains the mean, median, standard deviation, minimum, and maximum for the number of employees, the balance sheet size,and the premium volume of the insurance companies in the sample. These three variables serve as proxies for the firm size. In addition,location and dispersion statistics have been provided separately for the subsamples of cat bond investors and non-investors. The last threecolumns show the results of a Kolmogorov-Smirnov (K-S) test of the null hypothesis that the variables are normally distributed.

148

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EmpiricalAnalyses

No. of Employees Balance Sheet Size (mn EUR) Premium Volume (mn EUR)

N 44 N 44 N 44

Mann-Whitney U 218.0000 Mann-Whitney U 237.5000 Mann-Whitney U 249.0000

Standard Error 39.6440 Standard Error 39.6820 Standard Error 39.6850

p-value 0.8400 p-value 0.4880 p-value 0.3260

Table 17: Mann-Whitney U TestResults of a Mann-Whitney U test to assess whether the differences in the average number of employees, balance sheet size, and premiumvolume between investors and non-investors are statistically significant. The test is based on the null hypothesis that the two samples underconsideration have been drawn from the same distribution.

4.1

Descrip

tive

Statistics

149

Full Sample Investors Non-investors

Determinant relevant irrelevant sum relevant irrelevant sum relevant irrelevant sum

Expertise/Experience 15 21 36 8 4 12 7 17 24

in percent 41.67 58.33 100.00 66.67 33.33 100.00 29.17 70.83 100.00

Risk/Return/Correlation 16 20 36 10 2 12 6 18 24

in percent 44.44 55.56 100.00 83.33 16.67 100.00 25.00 75.00 100.00

Administrative Complexity 16 20 36 9 3 12 7 17 24

in percent 44.44 55.56 100.00 75.00 25.00 100.00 29.17 70.83 100.00

Data Availability 12 24 36 8 4 12 4 20 24

in percent 33.33 66.67 100.00 66.67 33.33 100.00 16.67 83.33 100.00

Regulatory Constraints 10 26 36 3 9 12 7 17 24

in percent 27.78 72.22 100.00 25.00 75.00 100.00 29.17 70.83 100.00

Accounting Issues 7 29 36 4 17 21 3 21 24

in percent 19.44 80.56 100.00 19.05 80.95 100.00 12.50 87.50 100.00

Table 18: Potential Determinants of the Investment DecisionNumbers and percentages of the insurance companies that stated whether or not a certain factor has influenced their decision to invest incat bonds. Due to the exclusion of cases with missing data, the overall sample size drops to N = 36.


charges and accounting issues, in contrast, have been declared to be irrel-

evant by both groups. This finding supports our expectation expressed in

Section 2.2 that these two aspects do not affect an insurance company’s

propensity to invest in cat bonds.

4.2 Determinants of the Cat Bond Investment

Decision

As explained in Section 3.4, before estimating the logistic regression

model, we run an EFA to extract a set of latent constructs from the ob-

served variables in our sample. For the resulting factor structure to be

meaningful and properly interpretable, the correlations between items

that are associated with the same factor should be high, while those

between items that represent different factors should be low. This idea

underlies the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy,

which indicates whether a data set is suitable for an EFA. Being defined

between zero and one, KMO values below 0.5 imply that EFA should not

be applied, whereas KMO values in excess of 0.8 mean that the sample

is particularly well suited for the analysis (see Kaiser, 1974). Following

an iterative process guided by the KMO measure, we identified 15 of

the 41 items as problematic and removed them from our sample. The

remaining 26 items lead to a solid KMO value of 0.7041. Furthermore,

in order to check the EFA precondition of normality, the K-S goodness-

of-fit test has been employed. Apart from very few exceptions, we do not

find significant deviations from the normal distribution, implying that

the items can be used in a factor analysis.37 Subsequently, we conduct

Bartlett’s test of sphericity and find the correlations of the items to be

statistically significant on the 1 percent level with a χ2 test statistic of

1,106.16 and 325 degrees of freedom. Since the EFA procedure relies on

the correlation (covariance) matrix of the observed variables to derive

the latent constructs, this test result is another indication for the suit-

ability of our data.

37Due to the standard nature of the K-S statistic and the multitude of variables,we decided not to report these results.

4.2 Determinants of the Cat Bond Investment Decision 151

For the initial factor extraction we choose the principal components

analysis. This procedure produces an orthogonal factor structure (i.e.,

the pairwise factor correlations are zero) by repeatedly searching for lin-

ear combinations of the items that account for the largest fraction of the

still unexplained variance, until the number of extracted factors equals

the number of items.38 The usual result is that, on the one hand, the

majority of items strongly load on the first few factors and, on the other

hand, substantial cross-loadings of items with more than one factor arise.

Consequently, it is common to rotate the extracted factor structure in

order to generate a more coherent pattern of loadings that considerably

improves interpretability.39 For this purpose, we resort to the orthogo-

nal varimax rotation approach, which repositions the axes of the factor

space such as to maximize the variance of the squared loadings per fac-

tor. Moreover, since EFA does not provide a theoretical foundation for

the number of factors to be retained, our hypotheses from Section 2.2

serve as the main guidance for the dimensionality of the model. In addi-

tion, we employ the Kaiser criterion, which states that only factors with

eigenvalues in excess of one should be retained.40

Table 19 summarizes the results of the EFA.41 As can be inferred

from the rotated factor loadings matrix, we decided in favor of a five-

factor model that is compatible with our hypotheses. This solution is

also supported by the Kaiser criterion (see eigenvalues).42 In sum, the

five factors account for more than 80 percent of the variation in the

38Taken together, the principal components explain the total variance of all items.39In rotated factor structures, most items tend to load relatively high on one factor,

while exhibiting rather weak cross-loadings with others.40Being defined as the sum of squared factor loadings across all items, eigenvalues

represent the amount of the total variance explained by a factor. As EFA is commonlyperformed with standardized variables, each item exhibits an eigenvalue of one. Thus,intuitively the Kaiser criterion requires factors to explain at least as much varianceas individual items.

41In order to enhance the readability and interpretability of this table, factor load-ings below 0.4000 have been suppressed.

42Note that there is actually a sixth factor, which exhibits an eigenvalue just slightlyabove one. However, it contributes a mere 3.85 percent of explained variance and isneither supported by our theory, nor clearly associated with a specific item battery.In addition, no item exhibits a loading in excess of 0.6 with regard to this factor.Hence, we chose not to include it in the final factor model.

152

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EmpiricalAnalyses

Item Factor 1 Factor 2 Factor 3 Factor 4 Factor 5

Cat bonds ...

... fit well in our portfolio 0.8440

... are compatible with our strategic ALM goals 0.9165

... are an attractive asset class 0.4792 0.4125 0.6470

Our firm ...

... is very experienced in the asset class 0.8706

... has a strong cat bond expertise 0.8930

... fully understands the typical risks 0.8171

... can handle the modeling/valuation/risk mgmt 0.9292

... possesses cat bond portfolio mgmt skills 0.8915

... understands the accounting treatment 0.8479

... understands the regulatory treatment 0.7481

... commands the necessary overall resources 0.9126

The following information is readily available:

– Transaction data 0.9066

– Pricing information 0.8346

– Historical performance figures 0.5494

– Loss experience 0.7486

– Deal documents 0.8976

– Overall cat bond data availability 0.9489

The cat bond asset class exhibits ...

... a strong historical performance 0.5020 0.8025

... an attractive return potential 0.7539

... a high relative value 0.8458

... an appealing overall risk-return profile 0.4828 0.7713

Cat bonds ...

... are standardized 0.6568 0.5616

... are liquid 0.8083

... are associated with low administration costs 0.4289 0.6631

... expose investors exclusively to insurance risk 0.8532

... are not associated with credit risk 0.7821

Eigenvalues 8.9929 6.7188 2.1114 1.9237 1.7278

Explained Variance (percent) 34.5879 25.8416 8.1209 7.3990 6.6455

Cumulative Explained Variance 34.5879 60.4295 68.5504 75.9494 82.5949

Cronbach’s α 0.9653 0.9318 0.9152 0.8761 0.8819

Table 19: Rotated Factor Loadings Matrix with Additional StatisticsFactor loadings resulting from an EFA for 26 items that have been measured on Likert scales. In order to enhance the readability and interpretability of this table,factor loadings below 0.4000 have been suppressed. In sum, the five factors explain 82.5949 percent of the total variance.


data. Furthermore, apart from two exceptions, all factor loadings that

belong to one item battery exceed 0.60, underlining a strong influence

of the common factors on the observed variables through which they

have been measured.43 This is also reflected by the low number of cross-

loadings above 0.4 as well as the high values for Cronbach’s alpha, which

measures the internal consistency of each factor. Thus, the 26 items that

have been included in the EFA lead to a meaningful factor structure. In

line with our arguments in Section 2.2, we interpret the five factors as

follows:

- Factor 1: expertise and experience with regard to the cat bond

asset class (hypothesis 3)

- Factor 2: perceived availability of data and information on the cat

bond asset class (hypothesis 7)

- Factor 3: perceived attractiveness of the risk-return profile (hy-

pothesis 4)

- Factor 4: perceived administrative complexity (hypothesis 6)

- Factor 5: perceived fit with the insurance company’s strategic

ALM goals (hypothesis 2)

This EFA output enables us to test five of our eight hypotheses within

a logistic regression analysis. In order to control for the remaining three

determinants postulated in Section 2.2, we need to draw on further in-

dependent variables. More specifically, 2 of the 15 items that were not

suited for the EFA have been averaged to form an additional factor, re-

flecting hypothesis 4 (diversification benefits of cat bonds). In addition,

we include the number of employees as a proxy for the firm size (hy-

pothesis 1).44 Finally, to account for hypothesis 8, we coded a dummy

variable for the regulatory constraints, which equals one if the company

is subject to Swiss investment rules and zero otherwise.

43The factor loadings can be interpreted as correlation coefficients between indica-tor variables and factors.

44We have also estimated alternative model specifications based on the balancesheet size and the premium volume to ensure that the reported significance level forthe size factor is robust with regard to the employed proxy.


The results for a logistic regression model, comprising these eight

independent variables, are shown in Table 20. Unreported collinearity

diagnostics such as the tolerance and the variance inflation factor (VIF)

indicate that multicollinearity is not an issue. The coefficients βi reflect

the magnitude of the effect of each independent variable on the logit,

exp(βi) represents the corresponding impact on the OR, and s.e. is the

standard error of the respective parameter. The Wald statistic is em-

ployed to test the significance of the individual logit coefficients. Exam-

ining the corresponding p-values and significance levels, we notice that

the coefficients of the regressors “expertise and experience”, “perceived

fit with the firm’s strategic ALM”, and “regulatory constraints” turn

out to be statistically significant.45 Consistent with the corresponding

hypotheses, the first two variables exhibit a positive impact, while the

last factor reduces the logit and the investment probability. All other fac-

tors, on the contrary, appear to be irrelevant with regard to the insurers’

decision to add cat bonds to their portfolios.

Table 20 also contains the typical goodness-of-fit measures for logistic

regression models. −2LL0 and −2LLm equal minus two times the log-

likelihood value for a null model that includes only a constant and minus

two times the log-likelihood value for the considered model, respectively.

The higher the value of −2LLm, the worse the actual model fit. Since

−2LLm (also known as deviance) is χ2-distributed with N−k−1 degrees

of freedom (k equals the number of explanatory variables), we can use

it to test the null hypothesis of a perfect model fit that, due to the p-

45Note that we also conducted analyses with the 13 spare items, which are neitherused in the EFA nor reflect a specific hypothesis. Five of these items cover more de-tailed aspects with regard to accounting treatment and solvency capital requirements,another five represent specific transactional characteristics such as TRS features andcollateral arrangements, and one asks for the respondents’ overall risk perception.Unreported logistic regression results indicate that none of these variables adds anyexplanatory power to the model. Furthermore, additional qualitative characteristicssuch as the company type (primary insurer vs reinsurer) or business line (life vsnonlife) have been tested via dummy variables. In this regard, we find that being areinsurance company exhibits a significant positive impact on the investment decision.However, this can be simply explained by the fact that the characteristic “reinsurer”is highly predictable through a combination of the factors expertise/experience as wellas perceived fit with the strategic ALM, and is thus already covered by our model.

4.2

Determ

inan

tsof

the

Cat

Bon

dIn

vestmen

tD

ecision155

N = 36 βi exp(βi) s.e. Wald p-value sig.

Constant 0.3867 1.4721 0.9034 0.1832 0.6686

Company Size –0.0002 0.9998 0.0001 1.6369 0.2008

Expertise and Experience 3.5537 34.9413 1.6473 4.6537 0.0310 **

Perceived Fit with Strategic ALM 3.0297 20.6905 1.4511 4.3591 0.0368 **

Perceived Data Availability 0.4424 1.5565 0.6264 0.4989 0.4800

Perceived Administrative Complexity –0.8880 0.4115 0.8645 1.0550 0.3044

Perceived Risk-Return Profile 0.1325 1.1416 0.6774 0.0382 0.8449

Perceived Diversification Benefits 0.5492 1.7319 0.6929 0.6283 0.4280

Regulatory Constraints –4.9872 0.0068 2.5702 3.7652 0.0523 *

Goodness of Fit χ2 df p-value

−2LL0 (null model) 45.8290 34 0.0847

−2LLm (considered model) 20.3100 26 0.7766

LR (likelihood ratio test) 25.5190 8 0.0013

HL (Hosmer-Lemeshow test) 10.2841 7 0.1730

Pseudo R2-measures

Cox and Snell 0.5078

Nagelkerke 0.7053

McFadden 0.5568

Table 20: Logistic Regression with all Potential DeterminantsResults for a logistic regression of the dichotomous dependent variable (investor/non-investor) on eight explanatory variables (plus constant).The coefficients βi indicate the magnitude of the effect of each independent variable on the logit, exp(βi) represents the corresponding impacton the OR, and s.e. is the standard error of the respective parameter. The Wald statistic is employed to test the significance of the logitcoefficients. Goodness of fit (based on the χ2 distribution): −2LL0 = minus two times the log-likelihood value for the null model (includesonly a constant); −2LLm = minus two times the log-likelihood value for the considered model (H0: perfect model fit); LR (likelihood ratio)equals the difference between −2LL0 and −2LLm (H0: all logit coefficients of the considered model are zero); HL = Hosmer-Lemeshowstatistic (H0: the observed and predicted event rates do not differ in each category of the dependent variable). Pseudo R2-measures aredefined between zero and one with values in excess of 0.4 indicating a good model fit. Significance levels: *** = 1 percent, ** = 5 percent,* = 10 percent.


value of 0.7766, cannot be rejected.46 A closely related statistic is the

likelihood ratio, LR, which equals the difference between −2LL0 and

−2LLm, thus providing a means for the assessment of the fit of the

considered model relative to the null model. It is also χ2-distributed

with degrees of freedom equal to the difference in the degrees of freedom

of −2LL0 and −2LLm and forms the basis for the likelihood ratio test.

In our case, the respective null hypothesis that all logit coefficients are

jointly zero can be rejected on the 1 percent significance level (p-value:

0.0013). Therefore, adding the tested regressors leads to a significant

improvement in the model fit compared to the null model. Furthermore,

we conduct the Hosmer-Lemeshow test. Based on the corresponding

variable HL, which is χ2-distributed with seven degrees of freedom, it is

not possible to reject the null hypothesis that the observed and predicted

event rates are equal for each category of the dependent variable. The

overall good model fit indicated by these statistics is further underlined

by the fact that the values of the pseudo R2-measures by Cox and Snell,

Nagelkerke, and McFadden are all above 0.4.47 Finally, turning to the

classification table (Table 21), we find that the model correctly predicts

83.33 percent of the investors, 95.83 percent of the non-investors, and

91.67 percent of all firms.48

Since all but three of the tested independent variables turned out to

be insignificant, we should be able to remove them without losing much

explanatory power. The results for such a reduced model, merely com-

prising the regressors “expertise and experience”, “perceived fit with

the firm’s strategic ALM goals”, and “regulatory constraints”, can be

found in Table 22. Again, the coefficients for these variables are statisti-

46We are aware that the −2LLm statistic is sensitive to the distribution of the casesamong the categories of the dependent variable. If the sample is very unbalanced inthis regard, it may provide a too optimistic assessment of the model fit.

47Although they cannot be interpreted exactly in the same way, pseudo R2-measures have been developed to mimic the well-known R2 of the linear regressionanalysis (see, e.g., Wooldridge, 2008). They equal zero if the independent variablesexhibit no explanatory power at all. Values above 0.4 indicate a good model fit.

48These figures are based on a cutoff value of 0.5, i.e., all firms for which theprobability of investing as implied by the model exceeds 0.5 are classified as investors.


Predicted

Observed Investor Non-investor % Correct

Investor 10 2 83.33

Non-investor 1 23 95.83

Overall 91.67

Table 21: Classification Table for Model with all Potential DeterminantsThis classification table can be employed to evaluate the predictive accuracy of the logisticregression model in Table 20. It shows how many of the observed values for the dichotomousdependent variable (investor/non-investor) are correctly predicted. The figures are basedon a cutoff value of 0.5, i.e., all firms for which the probability of investing as impliedby the model exceeds 0.5 are classified as investors. The model correctly predicts 83.33percent of the investors, 95.83 percent of the non-investors, and 91.67 percent of all cases.

cally significant.49 Moreover, as expected, the goodness-of-fit statistics

and pseudo R2-measures have hardly changed. Similarly, the figures re-

ported in the classification table for this new model (Table 23) suggest

a strong predictive accuracy. More specifically, although it includes five

independent variables less than the previous model, it still correctly pre-

dicts 83.33 percent of the investors, 83.33 percent of the non-investors,

and 83.33 percent of all firms in the sample.

To sum up, through our quantitative results, we are able to provide

evidence for hypotheses 2, 3, and 8. The remaining hypotheses, how-

ever, cannot be confirmed. Consequently, the expertise and experience

of insurance companies concerning cat bonds, the extent to which they

perceive a fit of the asset class with their strategic ALM goals, and the

prevailing regulatory regime seem to be the key determinants of the in-

vestment decision. To assess the importance of these factors relative to

each other, one needs to consider the respective effect strengths. Ac-

cording to the logit coefficient of 2.4740, the strongest impulse for an

investment in cat bonds emanates from the expertise/experience of a

company. With a corresponding value of 2.2814, however, the percep-

49Peduzzi et al. (1996) propose that as a rule of thumb, logistic regression modelsrequire a minimum of 10 events per explanatory variable to avoid biased regressioncoefficients and misestimation of the standard errors. Since the 36 participants inour sample comprise only 12 investors, we have additionally tested each of the threedeterminants in a separate model, thus increasing this ratio above the critical level.In doing so, we ensure the robustness of our results.

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EmpiricalAnalyses

N = 36 βi exp(βi) s.e. Wald p-value sig.

Expertise and Experience 2.4740 11.8694 0.9830 6.3336 0.0118 **

Perceived Fit with Strategic ALM 2.2814 9.7899 0.9887 5.3239 0.0210 **

Regulatory Constraints –3.3251 0.0360 1.4184 5.4955 0.0191 **

Goodness of Fit χ2 df p-value

−2LL0 (null model) 49.9070 35 0.0490

−2LLm (considered model) 24.9120 32 0.8096

LR (likelihood ratio test) 24.9950 2 0.0000

HL (Hosmer-Lemeshow test) 4.2433 7 0.7514

Pseudo R2-Measures

Cox and Snell 0.5006

Nagelkerke 0.6674

McFadden 0.5008

Table 22: Logistic Regression with Significant DeterminantsResults for a logistic regression of the dichotomous dependent variable (investor/non-investor) on three explanatory variables (withouta constant). The coefficients βi indicate the magnitude of the effect of each independent variable on the logit, exp(βi) represents thecorresponding impact on the OR, and s.e. is the standard error of the respective parameter. The Wald statistic is employed to test thesignificance of the logit coefficients. Goodness of fit (based on the χ2 distribution): −2LL0 = minus two times the log-likelihood value forthe null model (includes only a constant); −2LLm = minus two times the log-likelihood value for the considered model (H0: perfect modelfit); LR (likelihood ratio) equals the difference between −2LL0 and −2LLm (H0: all logit coefficients of the considered model are zero);HL = Hosmer-Lemeshow statistic (H0: the observed and predicted event rates do not differ in each category of the dependent variable).Pseudo R2-measures are defined between zero and one with values in excess of 0.4 indicating a good model fit. Significance levels: *** = 1percent, ** = 5 percent, * = 10 percent.

4.3 Further Qualitative Results 159

Predicted

Observed Investor Non-investor % Correct

Investor 20 4 83.33

Non-investor 2 10 83.33

Overall 83.33

Table 23: Classification Table for Model with Significant DeterminantsThis classification table can be employed to evaluate the predictive accuracy of the logisticregression model in Table 22. It shows how many of the observed values for the dichotomousdependent variable (investor/non-investor) are correctly predicted. The figures are basedon a cutoff value of 0.5, i.e., all firms for which the probability of investing as impliedby the model exceeds 0.5 are classified as investors. The model correctly predicts 83.33percent of the investors, 83.33 percent of the non-investors, and 83.33 percent of all cases.

tion that the asset class is in line with the strategic ALM goals has a

similarly large positive impact on the likelihood to invest. In contrast

to that, the binding regulatory constraints with regard to the tied assets

faced by Swiss companies strongly oppose these factors (logit coefficient:

–3.3251), causing a significant reduction of the investment probability.

Thus, Swiss insurers seem to be a lot less likely to invest in cat bonds

than EU-based firms, even if they exhibit the same values with regard

to the two aforementioned factors.

4.3 Further Qualitative Results

Open Survey Questions

To complement our inference statistics, we additionally included five

open questions in the questionnaire. Thereby, the participants were given

the opportunity to express opinions and ideas with regard to different

aspects of their cat bond investment decision. Overall, we obtained

38 responses to open questions from 24 different key informants. A

comprehensive list of quotations has been included in the Appendix.

For reasons of efficient reporting, we have grouped the answers in this

section based on their key messages. The respective results are shown in

Table 24. A total of 14 statements contain aspects that encourage the

firms to invest in cat bonds. Six of these, i.e., 15.79 percent of all com-

ments, are centered around the attractive risk-return profile of cat bonds

160

IV

EmpiricalAnalyses

Full Sample

No. Percent

Aspects encouraging cat bond investments

”Cat bonds offer attractive returns/have a low fundamental correlation with other asset classes.” 6 15.79

”It can be better to write cat bond business than to use the conventional market.” 6 15.79

”We are obtaining knowledge of the cat bond market to use these instruments in the future.” 2 5.26

Aspects opposing cat bond investments

”They do not fit with our asset and liability management.” 9 23.68

”We have not undertaken a particular effort due to regulatory constraints.” 6 15.79

”Missing know-how.” 4 10.53

Other reasons 2 5.26

Further comments 3 7.89

Table 24: Open QuestionsThis table gives an overview of the responses to the open questions in the survey. 24 participants have commented on different aspectsregarding their decision to invest or not to invest in cat bonds. The answers are categorized by aspects encouraging and aspects opposingcat bond investments. The percentage figures are based on a total of 38 responses to open questions.


as well as the low correlation with other asset classes. Since these fac-

tors were not found to be statistically significant in the logistic regression

analysis of Section 4.2, we need to assume that they are merely a decisive

factor for certain insurers but not for the majority of firms. In another

six responses (15.79 percent), the respective participants point out that

their their companies view cat bond investments as a means for market

expansion and to complement their traditional insurance business. This

is quite an interesting consideration, which has not been hypothesized

ex ante and was thus missing in our questionnaire design. Hence, for the

time being, we need to take into account that this might be an additional

determinant while leaving the confirmation of its statistical significance

for future research. Finally, two answers (5.26 percent) name the inten-

sion to acquire know-how about the cat bond market as the main reason

for the investment decision. This provides further support for the factor

expertise and experience, which has been identified as one of the main

drivers in the previous section.

Moreover, 21 answers brought forward reasons not to purchase cat

bonds. Since the majority of survey participants are non-investors (see

Table 15), it could be expected that the negative statements outnumber

the arguments in favor of an investment in this asset class. Consistent

with our statistical results, a lacking fit of cat bonds with regard to

the ALM considerations of the company is stressed in nine comments

(23.68 percent). Furthermore, in six (15.79 percent) responses the key

informants note that their firm refrains from cat bond investments due

to regulatory constraints. Particularly the FINMA guidelines regard-

ing “tied assets” are referred to several times, thus confirming our logis-

tic regression results for H8.50 Apart from these aspects, four answers

(10.53 percent) revolve around the missing expertise and experience that

would be needed to make adequate investment decisions with regard to

cat bonds. Again, this supports our previous findings with regard to

H3. Finally, the responses to the open survey questions also comprise a

50A penalization in terms of the Solvency II capital charges for cat risk, in contrast,is only criticized in a single response.


totally new aspect counted under “other reasons”.51 One company does

not seem to show any interest in cat bond investments because they want

to avoid losses due to perils that their stakeholders do not expect to be

part of their exposure. The fact that earthquakes in Japan would not

be associated with a purely European insurance company is mentioned

as an example in this context.

Most answers to the open survey questions help to underline and

further illustrate the results of our empirical analysis. Indeed, it appears

that a large number of the participants made comments that can be

associated with one of the three significant determinants identified in

Section 4.2. In addition to that, however, we were able to gather new

information with regard to the investment decision that could not be

captured by the preset items in the questionnaire. The aspects revealed

in this regard should be taken into account in future empirical research

on this topic.

Interviews with Managers of Dedicated Cat Bond Funds

In addition to the survey, we conducted structured interviews with the in-

vestment managers of four large and influential dedicated cat bond funds.

Together, their assets under management amount to approximately USD

7.73 billion, which represented 76.19 percent of the outstanding cat bond

volume in 2011 (see Guy Carpenter, 2011). Thus, our interview partners

possess information about a large part of the market and profound knowl-

edge of their clients’ investment decisions as well as the reasons behind

them. This characterizes them as key informants for our study. The

interviews were carried out in March and April 2012. All participants

received the same set of questions and were asked to answer either in

form of a telephone interview or in writing. The generally low level of

cat bond investments in the insurance industry (see Section 2.1) is also

reflected by the investor base of the considered funds. While two of them

do not have insurers among their current investors at all, the other two

51The second statement in the category “other reasons” refers to the low degreeof liquidity of cat bonds. This consideration is covered by factor 4 of the empiricalanalysis (perceived administrative complexity).


pointed out that less than 1 percent of their total client money comes

from the insurance industry. Several reasons for this phenomenon have

been provided by our interview partners.

One of them emphasizes that the regulatory constraints in Switzer-

land are the main factor behind the limited interest in cat bond invest-

ments shown by the local insurance industry. According to his clients,

FINMA insists on a strict separation of business lines. Companies that

are exclusively regulated as life or health insurers are not permitted to

invest in cat bonds at all, since this would be economically equivalent

to the underwriting of insurance contracts in the property and liability

sector. Nonlife insurers, in contrast, for which natural disaster risk is

part of their core business, do not face such an explicit restriction with

regard to the asset class. However, their potential for cat bond invest-

ments is still considerably constrained due to the tied asset investment

rules set by FINMA. This statement provides further support for H8.

Other explanations revolve around the determinant expertise and ex-

perience. Our interviewees find this aspect to be especially relevant in

times of market turbulence. Under such circumstances as during the

financial crisis in 2008, those insurance firms without an in-depth knowl-

edge about the cat bond market are the first to abandon their engage-

ment as investors. It has also been stated that there are a number of

reinsurers as well as large primary insurers with considerable cat bond

expertise and experience. When willing to invest, those firms only con-

sider direct investments. Smaller insurers, on the other hand, often lack

know-how with regard to the structures, the market, or certain catas-

trophe risks in general and thus, if at all, access the asset class through

dedicated cat bond funds. We view these arguments as an additional

confirmation of H3.

Furthermore, the question whether the risk-return and correlation

profiles of cat bonds have a certain impact on the investment decision

was affirmed during three of the interviews. This is in line with the state-

ments of some of the survey participants. Hence, those insurers that


actually invest in cat bonds might view the beneficial characteristics of

the asset class to be great enough to overcome some of the other factors

that exhibit a negative impact on their investment decision. Neverthe-

less, the corresponding determinants did not turn out to be statistically

significant in our empirical analysis, implying that one should be cau-

tious about a generalization of these opinions. Therefore, in the absence

of further evidence, H4 and H5 can still not be ultimately confirmed.

Similarly, three interview partners state that an improvement in the

availability of data and information on the cat bond asset class would be

likely to have a positive influence on the demand. In this context, they

point to a potentially severe conflict of interest. Since the asset manage-

ment of those insurance companies that act as cat bond investors needs

to assess prospective transactions, it desires as much publicly available

information as possible. The sponsor, in contrast, is interested in a high

level of discretion, particularly for indemnity deals, in order to avoid

that its competitors gain too much insight into its underwriting activ-

ities. Consequently, insurers seem to believe that they can get better

data on the actual exposure when they insure the risk rather than re-

lying on offering documents of cat bond transactions. Moreover, it has

been mentioned that substantial changes in the risk models of the major

analytics firms (RMS, EQECAT, AIR) negatively affect the interest in

the asset class, since investors generally tend to avoid cat bonds that are

perceived to hide a considerable amount of model risk. Although these

are interesting new insights, the insignificance of the respective factor

within the empirical analysis prevents the confirmation of H7.

Finally, the interviews revealed two perspectives concerning the cat

bond investment decision of insurance companies that had not been an-

ticipated in Section 2.2. Interestingly, these are consistent with the new

aspects that we identified based on the answers to the open survey ques-

tions. The first point, which has been mentioned by two of the intervie-

wees, can be described as political reasons for the decision not to buy

cat bonds. More specifically, although stakeholders might benefit from

this asset class through enhanced diversification, the management of in-

5 Summary and Conclusion 165

surance companies can be reluctant to accept exposures outside of their

core market due to the associated career risks. In doing so, they aim

to avoid the responsibility for losses due to natural hazards in locations

where their company is not even represented with its insurance opera-

tions. Apart from that, our interview partners indicated that some firms

have embraced cat bonds as a complement to their conventional business.

While some insurers exclusively approach the topic from an asset man-

agement perspective, others consider cat bond investments as a relative

value trade with regard to insurance products. If the pricing of a cat

bond issue is more attractive than that of a corresponding traditional

contract, these companies will switch to the former in order to benefit

from its superior risk-return trade-off.

5 Summary and Conclusion

Although they are familiar with the risks inherent in cat bonds, insur-

ance and reinsurance companies jointly account for less than ten percent

of the current demand in the market. In order to be able to develop

explanations for this phenomenon, a deeper insight into the underlying

decision-making process is needed. Accordingly, our main research goal

in this paper is to identify major determinants of the cat bond invest-

ment decision of insurers. For this purpose, we conducted a comprehen-

sive survey among senior executives in the European insurance industry.

Evaluating the corresponding data set by means of EFA and logistic

regression methodology, we are able to show that the firm’s expertise

and experience with regard to cat bond investments, their perceived fit

with its ALM philosophy, and the prevailing regulatory regime exert a

significant influence on an insurer’s propensity to invest. In contrast

to that, the perception of the asset class’s risk-return profile, diversifi-

cation benefits, administrative complexity, as well as the availability of

data and information on cat bond transactions seem to be of lesser rel-

evance. Similarly, we do not find evidence for an impact of firm size,

accounting treatment, or solvency capital requirements. These statisti-

cal results are complemented by further qualitative survey answers and

additional information from structured interviews with the investment


managers of four large dedicated cat bond funds.

Our findings should be highly relevant to cat bond issuers and policy-

makers alike. Since, in general, insurance companies represent a central

source of institutional investor demand in the capital markets, the re-

duction of existing investment barriers with regard to cat bonds could

generate a substantial growth impulse for this asset class. It appears

that, theoretically, issues relating to the first two determinants (lack of

expertise/experience, perceived fit with the strategic ALM goals) could

be simply overcome by properly educating prospective market partici-

pants and disseminating more information about the merits of adding

cat bond exposure to the balance sheet of a typical insurance company.

Particularly life insurers should be able to exploit the virtues of the in-

strument, since it may serve as a diversification tool for both their asset

and liability risks. Impediments arising due to regulatory constraints

such as the rigid legal investment guidelines set by FINMA, however,

seem a lot more difficult to address. In this respect, it might be helpful

to initiate an intensive dialogue with the regulators, highlighting that,

due to risk sharing and performance aspects, it may be economically

reasonable for insurance companies to allocate a certain fraction of their

asset portfolios to cat bonds.

Finally, future research could be aimed at overcoming some of the

limitations of our study. The most important aspect in this regard re-

lates to sample size. Indeed, it would be helpful to verify our results

based on a much broader survey, for example, including U.S. insurance

companies or even adopting a global scope. In addition, the qualitative

information that was gathered through open survey questions and struc-

tured interviews raised completely new aspects for which measurement

variables had not been incorporated in our original questionnaire design.

Hence, an examination of the statistical significance of these potential

determinants is still outstanding.

6 Appendix 167

6 Appendix

6.1 Aspects Encouraging Cat Bond Investments

Risk-Return Profile and Diversification Benefits

- Attractive returns.

(Germany; Reinsurer; Director)

- Decent expected return proposition.

(Finland; Primary Insurer; Portfolio Manager)

- Attractive returns.

(Switzerland; Reinsurer; Head of Nonlife Risk Transfor-

mation)

- Potentially attractive spreads.

(Switzerland; Primary Insurer)

- Cat bond returns typically have a low fundamental cor-

relation with other asset classes.


- Diversification.


Market Expansion/Complement the Traditional Insurance

Business

- For visibility in this market place – it can be better to

“write” cat bond business than to use the conventional

market.

(UK; Reinsurer; Managing Director)

- Market expansion.

(Italy; Primary Insurer; Managing Director)

- Certain risks are not available in form of traditional

reinsurance.


- Due to the evolution of the business it could be interest-

ing to invest in this asset class.

(Italy; Primary Insurer; Director)


- Market making.

(Switzerland; Reinsurer; Head of Nonlife Risk Transfor-

mation)

- Cat Bonds are the most liquid asset class inside the non-

life risk category.


Expertise and Experience with Regard to the Asset Class

- To test the market.

(Sweden; Reinsurer; Group CFO)

- Obtaining knowledge of the cat bond market to use these

instruments in the future.

(Netherlands; Primary Insurer; Senior Risk Manager)

6.2 Aspects Opposing Cat Bond Investments

Fit with Strategic Asset and Liability Management Goals

- At the moment, they do not exactly fit in our asset and

liability management.

(Italy; Primary Insurer)

- The decision not to invest in cat bonds is based on a

total balance sheet view and the regional risk profile of

our company.

(Switzerland; Primary Insurer; Director)

- We are very conservative in our investment approach.

(Greece; Primary Insurer)

- Do not fit our ALM considerations.

(Austria; Primary Insurer; Market Risk Manager)

- Main focus in matching liabilities.

(Finland; Primary Insurer; Chairman of the Board)

- Strategic decision. Ultimately, we do not want to buy

risks that we already insure.

(Switzerland; Primary Insurer; CIO)

6.2 Aspects Opposing Cat Bond Investments 169

- We do not treat them as investments, since they are

correlated with our key cat risks.


- We acquire our cat risk through reinsurance and feel no

need to buy it through assets.

(Portugal; Primary Insurer; CFO)

- As a reinsurer we are already exposed to natural dis-

asters risk. Investing in cat bonds would create a de-

pendency between our insurance results and investment

results.

(Belgium; Reinsurer; Member of the Executive Board)

Regulatory Constraints

- We have not undertaken a particular effort due to regu-

latory constraints.

(Switzerland; Primary Insurer; Head of Investments)

- Not allowed to invest according to FINMA rules guid-

ing “Gebundene Vermogen” (tied assets), therefore no

particular efforts undertaken.

(Switzerland; Primary Insurer; Head of Asset Manage-

ment)

- All our investments need to qualify for tied assets. Con-

sidering the local asset management knowledge/team, these

investments will not qualify as “tied assets” and hence

we cannot invest.

(Switzerland; Primary Insurer; Risk Manager)

- See FINMA regulation covering “Gebundene Vermogen”

(tied assets).

(Switzerland; Primary Insurer; Head of Investments)

- We maintain a very low risk profile, which ensures that

we meet the Swiss regulatory tied assets requirement.

(Switzerland; Primary Insurer; Controller)


- Under Solvency II, cat risk is heavily penalized in terms

of capital requirements.

(Portugal; Primary Insurer; CFO)

Expertise and Experience with Regard to the Asset Class

- Missing know-how.


- We are more confident in traditional investment asset

classes.


- Opacity: we have difficulties to properly value cat bonds.


- The risk exposures and the risk accumulation are diffi-

cult to assess and monitor.

(Switzerland; Primary Insurer; CIO)

Other Reasons

- Although the risk-return profile is very interesting, it can

be difficult to explain to our stakeholders that we could

have made a loss due to a peril that our stakeholders

don’t expect to be our risk. For example, a Japanese

earthquake is not a peril that our stakeholders expect to

cause a loss for an insurer only active in Europe.

(Netherlands; Primary Insurer; Senior Risk Manager)

- Not very liquid

(Italy; Primary Insurer; Managing Director)

6.3 Further Comments

- We have only invested in a cat bond fund that has no

specific restrictions.

(Italy; Primary Insurer)

6.3 Further Comments 171

- Our ILS investments are not covered by our ordinary as-

set management activities but are managed by our ded-

icated ILS department, which is part of the reinsurance

division.


- The entity in our group that holds cat bonds is a Bermu-

dian affiliate.



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Curriculum Vitae

Personal Information

Name: Katja Muller

Date of Birth: 27th of August 1986

Place of Birth: Berlin, Germany

Nationality: German

Education

01/2011 − present University of St. Gallen (HSG), St. Gallen, Switzerland

Doctoral Studies in Management

08/2008 − 05/2009 Florida Institute of Technology, Melbourne, USA

Master of Science in Applied Mathematics

10/2005 − 11/2010 University of Ulm, Ulm, Germany

Diplom-Wirtschaftsmathematikerin

09/1991 − 06/2000 Grosse Schule, Wolfenbuttel, Germany

Abitur (A-Levels)

Work Experience

01/2011 − present Institute of Insurance Economics

University of St. Gallen, Switzerland

Project Manager and Research Associate


Teaching Assistant

08/2008 − 05/2009 Florida Institute of Technology, Melbourne, USA

Teaching Assistant


Teaching Assistant

02/2006 − 03/2006 Siemens AG, Braunschweig, Germany

Intern, Rail Automation

Documents

Essays on Insurance Management - University of St. …...Essays on Insurance Management — The Theory of Insurance Fraud and Empirical Analyses of Auditing Strategies and Cat Bond