Arthur Charpentier, Insurance: Risk Pooling and Price Segmentation - 2017 Insurance: Risk Pooling and Price Segmentation — Using Information in a ‘Big Data’ Context — A. Charpentier (Université de Rennes 1) Bank of England, London November 2017 @freakonometrics freakonometrics freakonometrics.hypotheses.org 1
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Insurance: Risk Pooling and Price Segmentation
Using Information in a Big Data Context A. Charpentier (Universit
de Rennes 1)Bank of England, LondonNovember 2017@freakonometrics
freakonometrics freakonometrics.hypotheses.org
1https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Brief IntroductionA. Charpentier (Universit de
Rennes 1)Professor Economics Department, Universit de Rennes
1Director Data Science for Actuaries Program, Institute of
Actuaries(previously Actuarial Sciences, UQM & ENSAE
Paristechactuary in Hong Kong, IT & Stats FFA)PhD in Statistics
(KU Leuven), Fellow of the Institute of ActuariesMSc in Financial
Mathematics (Paris Dauphine) & ENSAEResearch Chair :ACTINFO
(valorisation et nouveaux usages actuariels de linformation)Editor
of the freakonometrics.hypotheses.orgs blogEditor of Computational
Actuarial Science, CRCAuthor of Mathmatiques de lAssurance Non-Vie
(2 vol.), Economica@freakonometrics freakonometrics
freakonometrics.hypotheses.org
2http://freakonometrics.hypotheses.orghttps://www.crcpress.com/Computational-Actuarial-Science-with-R/Charpentier/p/book/9781138033788https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Insurance vs. Creditclick to visualize the
construction@freakonometrics freakonometrics
freakonometrics.hypotheses.org
3https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Insurance Pricing in a NutshellInsurance is the
contribution of the many to the misfortune of the fewFinance: risk
neutral valuation = EQ[S1F0] = EQ0[S1], where S1 =
N1i=1YiInsurance: risk sharing (pooling) = EP[S1]or, with
segmentation / price differentiation () = EP[S1 = ] for
some(unobservable?) risk factor imperfect information given some
(observable) risk variables X = (X1, , Xk)(x) = EP[S1X = x] = EPX
[S1|x]Insurance pricing is not only data driven, it is also
essentially model driven (seePricing Game)@freakonometrics
freakonometrics freakonometrics.hypotheses.org
4https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Insurance Pricing in a NutshellPremium is =
EPX[S1]It is datadriven (or portfolio driven) since PX is based on
the portfolio.click to visualize the construction@freakonometrics
freakonometrics freakonometrics.hypotheses.org
5https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Insurance Pricing in a NutshellPremium is E[S1|X
= x]= E[Ni=1YiX = x]= E [N |X = x] E [Yi|X = x]Statistical and
modeling issues to approximate based on some training datasets,with
claims frequency {ni,xi} and individual losses {yixi} depends on
the model used to approximate E [N |X = x] and E [Yi|X = x] depends
on the choice of meta-parameters depends on variable selection /
feature engineeringTry to avoid overfit@freakonometrics
freakonometrics freakonometrics.hypotheses.org
6https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Risk Sharing in InsuranceImportant formula E[S]=
E[E[S|X]and its empirical version1nni=1Si 1nni=1(Xi) (as n, from
the law of large number)interpreted as on average what we pay
(losses) is the sum of what we earn(premiums).This is an ex-post
statement, where premiums were calculated ex-ante.@freakonometrics
freakonometrics freakonometrics.hypotheses.org
7https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Risk Transfert without SegmentationInsured
InsurerLoss E[S] S E[S]Average Loss E[S] 0Variance 0 Var[S]All the
risk - Var[S] - is kept by the insurance company.Remark: all those
interpretation are discussed in Denuit & Charpentier
(2004).@freakonometrics freakonometrics
freakonometrics.hypotheses.org
8https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Insurance, Risk Pooling and SolidarityLa Nation
proclame la solidarit et lgalit de tous les Franais devant
lescharges qui rsultent des calamits nationales (alina 12, prambule
de laConstitution du 27 octobre 1946)31 zones TRI (Territoires
Risques dInondation) on the left, and flooded
areas.@freakonometrics freakonometrics
freakonometrics.hypotheses.org
9http://www.rhone-mediterranee.eaufrance.fr/docs/dir-inondations/cartes/Carte_TRI_retenu_RhoM.pdfhttps://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Insurance, Risk Pooling and SolidarityHere is a
map with a risk score -{1, 2, , 6} scaleOne can look at Lorenz
curveSouth Other Total% portfolio 11% 89% 100%% claims 51% 49%
100%Premium 463 55 100@freakonometrics freakonometrics
freakonometrics.hypotheses.org
10https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Risk Transfert with Segmentation and Perfect
InformationAssume that information is observable,Insured
InsurerLoss E[S|] S E[S|]Average Loss E[S] 0Variance
Var[E[S|]]Var[S E[S|]]Observe that Var[S E[S|]]= E[Var[S|]], so
thatVar[S] = E[Var[S|]] insurer+Var[E[S|]] insured.@freakonometrics
freakonometrics freakonometrics.hypotheses.org
11https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Risk Transfert with Segmentation and Imperfect
InformationAssume that X is observableInsured InsurerLoss E[S|X] S
E[S|X]Average Loss E[S] 0Variance
Var[E[S|X]]E[Var[S|X]]NowE[Var[S|X]]= E[E[Var[S|]X]]+
E[Var[E[S|]X]]= E[Var[S|]] pooling+E{Var[E[S|]X]}
solidarity.@freakonometrics freakonometrics
freakonometrics.hypotheses.org
12https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Risk Transfert with Segmentation and Imperfect
InformationWith imperfect information, we have the popular risk
decompositionVar[S] = E[Var[S|X]]+ Var[E[S|X]]= E[Var[S|]]
pooling+E[Var[E[S|]X]] solidarity insurer+Var[E[S|X]]
insured.@freakonometrics freakonometrics
freakonometrics.hypotheses.org
13https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017More and more price differentiation ?Consider 1
= E[S1]and 2(x) = E[S1|X = x]Observe that E[(X)]=xX(x) P[x]=xX1(x)
P[x] +xX2(x) P[x] Insured with x X1 : choose Ins1 Insured with x
X2: choose Ins2Ins1:xX11(x) P[x] 6= E[S|X X1]Ins2:xX22(x) P[x] =
E[S|X X2]@freakonometrics freakonometrics
freakonometrics.hypotheses.org
14https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Price Differentiation, a Toy ExampleClaims
frequency Y (average cost = 1,000)X1Young Experienced Senior
TotalX2Town12%(500)9%(2,000)9%(500)9.5%(3,000)Outside8%(500)6.67%(1,000)4%(500)6.33%(2,000)Total10%(1,000)8.22%(3,000)6.5%(1,000)8.23%(5,000)from
C., Denuit & lie (2015)@freakonometrics freakonometrics
freakonometrics.hypotheses.org
15https://f.hypotheses.org/wp-content/blogs.dir/253/files/2015/10/Risques-Charpentier-Denuit-Elie.pdfhttps://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Model Comparison (and Inequalities)Use of
statistical techniques to get price differentiationsee discriminant
analysis, Fisher (1936)In human social affairs, discrimination is
treatment orconsideration of, or making a distinction in favor of
oragainst, a person based on the group, class, or categoryto which
the person is perceived to belong rather thanon individual
attributes (wikipedia)For legal perspective, see Canadian Human
Rights Act@freakonometrics freakonometrics
freakonometrics.hypotheses.org
18http://onlinelibrary.wiley.com/doi/10.1111/j.1469-1809.1936.tb02137.x/abstract;jsessionid=DBF4533A7EFB45D5CF8EDA619AC8EE3F.f02t02https://en.wikipedia.org/wiki/Discriminationhttps://en.wikipedia.org/wiki/Canadian_Human_Rights_Acthttps://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Model Comparison and Lorenz curvesSource:
Progressive Insurance@freakonometrics freakonometrics
freakonometrics.hypotheses.org
19https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Model Comparison and Lorenz curvesConsider an
ordered sample {y1, , yn} of incomes,with y1 y2 yn, then Lorenz
curve is{Fi, Li} with Fi =inand Li =ij=1 yjnj=1 yjWe have observed
losses yi and premiums (xi). Con-sider an ordered sample by the
model, see Frees, Meyers& Cummins (2014), (x1) (x2) (xn),
thenplot{Fi, Li} with Fi =inand Li =ij=1 yjnj=1 yj0 20 40 60 80
100020406080100Proportion (%)Income (%)poorest richest0 20 40 60 80
100020406080100Proportion (%)Losses (%)more risky less
risky@freakonometrics freakonometrics
freakonometrics.hypotheses.org
20http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2438129http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2438129https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Model Comparison for Life Insurance
ModelsConsider the case of a death insurance contract, thatpays 1
if the insured deceased within the year.(x) = E[Tx t+ 1|Tx > t]
No price discrimination = E[(X)] Perfect discrimination (x)
Imperfect discrimination = E[(X)|X < s] and + = E[(X)|X >
s]click to visualize the construction@freakonometrics
freakonometrics freakonometrics.hypotheses.org
21https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017From Econometric to Machine Learning
TechniquesIn a competitive market, insurers can use different sets
of variables and differentmodels, e.g. GLMs, Nt|X P(X t) and Y |X
G(X , )j(x) = E[N1X = x] E[Y X = x] = exp(Tx) Poisson P(x) exp(Tx)
Gamma G(X ,)that can be extended to GAMs,j(x) = exp(dk=1sk(xk))
Poisson P(x) exp(dk=1tk(xk)) Gamma G(X ,)or some Tweedie model on
St (compound Poisson, see Tweedie (1984)) conditionalon X (see C.
& Denuit (2005) or Kaas et al. (2008)) or any other statistical
modelj(x) where j argminmFj :XjR{ni=1`(si,m(xi))}@freakonometrics
freakonometrics freakonometrics.hypotheses.org
22https://www.ams.org/mathscinet-getitem?mr=786162https://www.economica.fr/livre-mathematiques-de-l-assurance-non-vie-tome-ii-tarification-et-provisionnement-denuit-michel-charpentier-arthur,fr,4,9782717848601.cfmhttp://www.springer.com/us/book/9783540709923https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017From Econometric to Machine Learning
TechniquesFor some loss function ` : R2 R+ (usually an L2 based
loss, `(s, y) = (s y)2since argmin{E[`(S,m)], m R} is E(S),
interpreted as the pure premium).For instance, consider regression
trees, forests, neural networks, or boostingbased techniques to
approximate (x), and various techniques for variableselection, such
as LASSO (see Hastie et al. (2009) or C., Flachaire & Ly (2017)
fora description and a discussion).With d competitors, each insured
i has to choose among d premiums,i =(1(xi), , d(xi))
Rd+.@freakonometrics freakonometrics freakonometrics.hypotheses.org
23http://www.springer.com/us/book/9780387848570https://hal.archives-ouvertes.fr/hal-01568851https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Insurance and Risk Segmentation: Pricing
Game@freakonometrics freakonometrics freakonometrics.hypotheses.org
24https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017A Game with Rules... but no GoalTwo datasets : a
training one, and a pricing one(without the losses in the
later)Step 1 : provide premiums to all contracts inthe pricing
datasetStep 2 : allocate insured among playersSeason 1 13
playersSeason 2 14 playersStep 3 [season 2] : provide additional
informa-tion (premiums of competitors)Season 3 23 players (3
markets, 8+8+7)Step 3-6 [season 3] : dynamics, 4
years@freakonometrics freakonometrics
freakonometrics.hypotheses.org
38https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Pricing Game in 2015Insurer 4GLM for frequency
and standardcost (large claimes were removed,above 15k),
Interaction Age andGenderActuary working for a mutuelle
com-panyInsurer 11Use of two XGBoost models (bodilyinjury and
material), with correctionfor negative premiumsActuary working for
a private insur-ance companyA1 A2 A3 A4 A5 A6 A7 A8 A9 A11
A13Market Share (in %)0246810A1 A2 A3 A4 A5 A6 A7 A8 A9 A11 A13Loss
Ratio (in %)050100150200A1 A2 A3 A4 A5 A6 A7 A8 A9 A11 A13Market
Share (in %)0246810A1 A2 A3 A4 A5 A6 A7 A8 A9 A11 A13Loss Ratio (in
%)050100150200@freakonometrics freakonometrics
freakonometrics.hypotheses.org
39https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Pricing Game in 2017Insurer 6 (market 3)Team of
two actuaries (degrees in Engineering and Physics), in
Vancouver,Canada. Used GLMs (Tweedie), no territorial
classification, no use ofinformation about other
competitorsSegments with high market share and low loss ratios were
also given somepremium increaseYearRatio of Quantiles of
Premiums1251020501001 2 3 4699% vs 1%95% vs 5%@freakonometrics
freakonometrics freakonometrics.hypotheses.org
40https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Pricing Game in 2017Insurer 7 (market 1)Actuary
in France, used random forest for variable selection, and
GLMsYearRatio of Quantiles of Premiums1251020501001 2 3 4799% vs
1%95% vs 5%Year (market 1)Loss Ratio (%)801001201401601802002201 2
3 47Year (market 1)Market Share (%)0102030401 2 3
47@freakonometrics freakonometrics freakonometrics.hypotheses.org
41https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Pricing Game in 2017Insurer 15 (market
2)Actuary,working as a consultant, Margin Method with iterations,
MS Access &MS ExcelYearRatio of Quantiles of
Premiums1251020501001 2 3 41599% vs 1%95% vs 5%Year (market 2)Loss
Ratio (%)801001201401601802002201 2 3 415Year (market 2)Market
Share (%)0102030401 2 3 415@freakonometrics freakonometrics
freakonometrics.hypotheses.org
42https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Pricing Game in 2017Insurer 21 (market
1)Actuary, working as a consultant, used GLMs, with variable
selection usingLARS and LASSOIterative learning algorithm (codes
available on github)YearRatio of Quantiles of Premiums1251020501001
2 3 42199% vs 1%95% vs 5%Year (market 1)Loss Ratio
(%)801001201401601802002201 2 3 421Year (market 1)Market Share
(%)0102030401 2 3 421@freakonometrics freakonometrics
freakonometrics.hypotheses.org
43https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Pricing Game in 2017Insurer 4 (market 2)Actuary,
working as a consultat,used XGBOOST, used GLMs for year 3.YearRatio
of Quantiles of Premiums1251020501001 2 3 4499% vs 1%95% vs 5%Year
(market 2)Loss Ratio (%)801001201401601802002201 2 3 44Year (market
2)Market Share (%)0102030401 2 3 44@freakonometrics freakonometrics
freakonometrics.hypotheses.org
44https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Pricing Game in 2017Insurer 8 (market
3)Mathematician, working on Solvency II sofware in
AustriaGeneralized Additive Models with spatial
variable@freakonometrics freakonometrics
freakonometrics.hypotheses.org
45https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Cluster, Segmentation and (Social)
NetworksSocial networks could be used to get additional information
about insuredpeople...Why not using social networks to create
(more) solidarity ?@freakonometrics freakonometrics
freakonometrics.hypotheses.org
46https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Cluster, Segmentation and (Social)
NetworksHomophily is the tendency of individuals to associate and
bond with similarothers, birds of a feather flock togetherfrom
Moody (2001) Race, School Integration and Friendship Segregation in
America@freakonometrics freakonometrics
freakonometrics.hypotheses.org
47http://www.soc.duke.edu/~jmoody77/ajs_reprint.pdfhttps://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Cluster, Segmentation and (Social) NetworksSo
far, risk classes are based on covari-atesX, correlated (causal
effect?) withclaims occurence (or severity).Why not consider
clusters in (social)networks, too?A lot of cofounding variables
(age, pro-fession, location, etc.)See InsPeer
experience.AlysArrynElysWaynwoodJasperArrynJeyneRoyceJonArrynLysaArrynRobertArrynRowenaArrynCassanaBaratheonCerseiLannisterJaimeLannisterJoffreyBaratheonMargaeryTyrellMyrcellaBaratheonOrmundBaratheonRenlyBaratheonRhaelleTargaryenRobertBaratheonSelyseFlorentShireenBaratheonStannisBaratheonSteffonBaratheonTommenBaratheonAmareiCrakehallAmereiFreyBenfreyFreyBethanyRosbyCleosFreyDornaSwyftEdmureTullyEmmonFreyGennaLannisterJeyneDarryJyannaFreyKevanLannisterLancelLannisterLyonelFreyMarissaFreyMariyaDarryMelesaCrakehallMerrettFreyOlyvarFreyPateoftheBlueForkPerraRoycePerwynFreyRooseBoltonRoslinFreyTionFreyTywinFreyWaldaFreydaughterofMerrettWalderFreyWalderFreysonofEmmonWalderFreysonofMerrettWillamenFreyWillemFreyAeronGreyjoyAlannysHarlawAsha(Yara)GreyjoyBalonGreyjoyDonelGreyjoyErikIronmakerEuronGreyjoyHarlonGreyjoyLadyofHousePiperLadyofHouseStonetreeLadyofHouseSunderlyMaronGreyjoyQuellonGreyjoyQuentonGreyjoyRobinGreyjoyRodrikGreyjoyTheonGreyjoyUrrigonGreyjoyVictarionGreyjoyAlysStackspear
AlysanneFarmanAntarioJastCerennaLannisterCerissaBraxDamionLannisterDamonLannisterDamonLannistersonofJasonDarlessaMarbrandDavenLannisterEllaLannisterErmesandeHayfordGerionLannisterGeroldLannisterJasonLannisterJeyneMarbrandJoannaLannisterLannaLannisterLucionLannisterMarlaPresterMyrandaLeffordMyrielleLannisterRohanneWebberSansaStarkShieraCrakehallStaffordLannisterTeoraKyndallTyboltLannisterTygettLannisterTyrekLannisterTyrionLannisterTyshaTytosLannisterTywinLannisterWillemLannisterAegonTargaryensonofRhaegarDoranMartellDoreaSandEliaMartellEliaSandEllariaSandLorezaSandMellarioofNorvosMorsMartellbrotherofDoranNymeriaSandObaraSandObellaSandOberynMartellPrincessofDorneRhaegarTargaryenRhaenysTargaryendaughterofRhaegarSarellaSandTyeneSandAlysKarstarkArraNorreyArtosStarkAryaFlintAryaStarkBenjenStarkBeronStarkBranStarkBrandonStarkBrandonStarkBurnerBrandonStarksonofCreganCatelynStarkCreganStarkEddardStarkEdwyleStarkGillianeGloverJeyneWesterlingJonSnowJonnelStarkLorraRoyceLyannaGloverLyannaStarkLyarraStarkLynaraStarkLysaraKarstarkMarnaLockeMelanthaBlackwoodMyriameManderlyRamsayBoltonRickardStarkRickonStarkRickonStarksonofBenjenRobbStarkRobynRyswellRodrikStarkRodrikStarksonofBeronRodwellStarkTalisaStarkWillamStarkAegonVTargaryenAerysIITargaryenBethaBlackwoodDaenerysTargaryenDrogoDuncanTargaryenDyannaDayneHizdahrzoLoraqJaehaerysIITargaryenJennyofOldstonesMaekarITargaryenMaronMartellRhaellaTargaryenShaeraTargaryenViserysTargaryenHosterTullyMinisaWhentPetyrBaelishAlerieHightowerElinorTyrellElynNorridgeGarlanTyrellHobberRedwyneHorasRedwyneLeoBlackbarLeonetteFossowayLiaSerryLorasTyrellLuthorTyrellLuthorTyrellsonofMorynLuthorTyrellsonofTheodoreMaceTyrellMedwickTyrellMinaTyrellMorynTyrell
OleneTyrellOlennaRedwynePaxterRedwyneTheodoreTyrellUnknownfatherTyrellUnknownmotherTyrellWillasTyrellvia
shiring.github.io@freakonometrics freakonometrics
freakonometrics.hypotheses.org
48https://www.inspeer.me/https://shiring.github.io/networks/2017/05/15/got_finalhttps://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017(Social) Networks and CreditUsed already on
credit(see cnn or or digitaltrends)E.g Lenddo or LendupIt does mean
that homophily can be seenas a substitute to standard credit
explana-tory variales...@freakonometrics freakonometrics
freakonometrics.hypotheses.org
49http://money.cnn.com/2015/08/04/technology/facebook-loan-patent/index.htmlhttps://www.digitaltrends.com/mobile/banks-track-loan-applicants-web-use/https://www.forbes.com/sites/tomgroenfeldt/2015/01/29/lenddo-creates-credit-scores-using-social-media/#424378fc2fdehttp://www.investopedia.com/articles/personal-finance/040715/lendup-responsible-alternative-payday-loans.asphttp://money.cnn.com/2015/08/04/technology/facebook-loan-patent/index.htmlhttps://www.digitaltrends.com/mobile/banks-track-loan-applicants-web-use/https://www.forbes.com/sites/tomgroenfeldt/2015/01/29/lenddo-creates-credit-scores-using-social-media/#424378fc2fdehttp://www.investopedia.com/articles/personal-finance/040715/lendup-responsible-alternative-payday-loans.asphttps://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Information and NetworksBut other kinds of
networks can be used, e.g. (genealogical) treesSee Ewen Gallics
ongoing work (actinfo chair).@freakonometrics freakonometrics
freakonometrics.hypotheses.org
50https://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
Arthur Charpentier, Insurance: Risk Pooling and Price
Segmentation - 2017Privacy IssuesSee General Data Protection
Regulation (EU 2016/679) : what about aggregation ?Consider a
population {1, , n} and a partition {I1, , Ik} (e.g.
geographicalareas Z), with respective sizes {n1, , nk}. Set Y j
=1njiIjYi.For continous covariates, set Xk,j =1nkiIjXk,i,For
categorical variables, consider the associate composition
variableXk,j = (Xk,1,j , , Xk,dk,j) where Xk,`,j =1nkiIj1(Xk,i =
`).See e.g. C. & Pigeon (2016) on micro-macro models and Enora
Belzs ongoingwork.@freakonometrics freakonometrics
freakonometrics.hypotheses.org
51https://en.wikipedia.org/wiki/General_Data_Protection_Regulationhttps://twitter.com/freakonometricshttps://freakonometrics.github.io/https://freakonometrics.hypotheses.org/
