Upload
dayna-griffin
View
215
Download
1
Embed Size (px)
Citation preview
Levels of Determinism in Workers’ Compensation
Reinsurance Commutations[PCAS 1999]
Gary Blumsohn
Arch Reinsurance [email protected]
CARe Seminar: September 17, 2003
Complete determinism:Know the future
Complete determinism:Know the future
Levels of Determinism
No determinism:Don’t know distributions
No determinism:Don’t know distributions
Stochastic determinism:Know the future statistically
Stochastic determinism:Know the future statistically
Refresher Example
Annual indemnity = $0
Annual medical = $200
10% annual medical inflation
Life expectancy = 2 years
Reinsurance layer: $500 xs $500
Method 1:Totally Deterministic
Payments:
Year 1 = $200
Year 2 = $220
Total at life expectancy = $420
=> Layer loss = $0
Method 2:Stochastic Mortality
YearAnnual
PaymentsCumulativePayments
LayerLoss
Prob. OfSurviving
ExpectedPayment
1 200 200 0 90% 0
2 220 420 0 70% 0
3 242 662 162 40% 65
Total 662 162 65
PV (5%) 614 140 56
Complete determinism:Know the future
Complete determinism:Know the future
No determinism:Don’t know distributions
No determinism:Don’t know distributions
Stochastic determinism:Know the future statistically
Stochastic determinism:Know the future statistically
Method 1Method 1
Method 2Method 2
Method 3Method 3
Realistic Example
35-year old male paraplegic
Paid to date: $370,000
Realistic Example (Cont.)
Annual indemnity: $20,000
Annual medical: $70,000
COLA: 4.1%
Medical inflation: 5.25%
Risk-adjusted discount rate: 5.36% (= inflation +
1.25%)
Method 1:Totally Deterministic
Total nominal payments: $11.2 million
Nominal PV
$0.5MM xs $0.5MM 500 413
$5MM xs $10MM 1,606 217
Higher layers 0 0
All layers 11,236 3,430
Method 2:Stochastic Date of Death
Total nominal payments: $13.9 million
Nominal PV
$0.5MM xs $0.5MM 495 409
$5MM xs $10MM 2,575 311
$10MM xs $50MM 3 0.1
Higher layers 0 0
All layers 14,900 3,408
Risks
Long life High inflation High medical usage Low investment income
Example
MedicalInflation Rate
Value of Layer$10MM xs
$70MM
0.00% $0
5.25% $0
10.5% $323,000
Order of Inflation Matters
High inflation today
=> higher nominal amounts forever
Method 3:Stochastic Economic Factors and Medical Costs
Stochastic models for Inflation (COLA)Medical inflation (related to inflation)Annual medical usageRisk-adjusted investment yield
(inflation-indexed bonds)
Method 3
Total nominal payments: $16.9 million
Nominal PV
$0.5MM xs $0.5MM 494 415
$5MM xs $10MM 2,591 344
$10MM xs $50MM 316 11
Higher layers 549 14
All layers 16,881 3,719
Commutation Values
0
100
200
300
400
500
0.5 xs 0.5 5 xs 10 xs 15
Method 1
Method 2
Method 3
Still Deterministic
Model parameters Model structure
Complete determinism:Know the future
Complete determinism:Know the future
No determinism:Don’t know distributions
No determinism:Don’t know distributions
Stochastic determinism:Know the future statistically
Stochastic determinism:Know the future statistically
Method 1Method 1
Method 2Method 2
Method 3Method 3
Next step:Judgmental leap
Next step:Judgmental leap
Complete determinism:Know the future
Complete determinism:Know the future
Economic Perspective on Levels of Determinism
No determinism:Don’t know distributions
No determinism:Don’t know distributions
Stochastic determinism:Know the future statistically
Stochastic determinism:Know the future statistically
PerfectKnowledge
PerfectKnowledge
RiskRisk
UncertaintyUncertainty
Uncertainty“30 years ago agents knew with certainty the price charged for a given product in both the
current period and in all future periods; today… they are likely to know the probability
distribution of current prices and the underlying stochastic structure that generates
future prices…. None of these approaches, however, captures the idea of ignorance.”
Gerald O’Driscoll & Mario Rizzo (1985)
“Austrian” Economics
Uncertainty Disequilibrium Market as a process, not an end state
“If you cannot measure,
your knowledge is meager
and unsatisfactory.”
Lord Kelvin
The Dilemma of the “Austrian” Actuary
Your knowledge is meager and unsatisfactory,
but you must make a recommendation.
Frank Knight, on the practical meaning of Kelvin’s statement for social scientists:
“If you cannot measure,
measure anyhow.”
Don’t ignore unmeasurables
that bias results.
Measuring the Unmeasurable
Fraction of previous layer?
What would breach layer?
Capacity charge?