Levels of Determinism in Workers’ Compensation Reinsurance Commutations [PCAS 1999]

1. Levels of Determinism in Workers’ Compensation Reinsurance Commutations[PCAS 1999] Gary Blumsohn Arch Reinsurance Company gblumsohn@archreco.com CARe Seminar: September 17, 2003

2. Levels of Determinism Complete determinism: Know the future Stochastic determinism: Know the future statistically No determinism: Don’t know distributions

3. Refresher Example • Annual indemnity = $0 • Annual medical = $200 • 10% annual medical inflation • Life expectancy = 2 years • Reinsurance layer: $500 xs $500

4. Method 1:Totally Deterministic Payments: Year 1 = $200 Year 2 = $220 Total at life expectancy = $420 => Layer loss = $0

5. Method 2:Stochastic Mortality

6. Method 1 Complete determinism: Know the future Method 2 Method 3 Stochastic determinism: Know the future statistically No determinism: Don’t know distributions

7. Realistic Example • 35-year old male paraplegic • Paid to date: $370,000

8. 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%)

9. 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

10. 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

11. Risks • Long life • High inflation • High medical usage • Low investment income

12. Example

13. Order of Inflation Matters High inflation today => higher nominal amounts forever

14. Method 3:Stochastic Economic Factors and Medical Costs • Stochastic models for • Inflation (COLA) • Medical inflation (related to inflation) • Annual medical usage • Risk-adjusted investment yield (inflation-indexed bonds)

15. 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

16. Commutation Values

17. Still Deterministic • Model parameters • Model structure

18. Method 1 Complete determinism: Know the future Method 2 Method 3 Stochastic determinism: Know the future statistically Next step: Judgmental leap No determinism: Don’t know distributions

19. Economic Perspective on Levels of Determinism Complete determinism: Know the future Perfect Knowledge Stochastic determinism: Know the future statistically Risk No determinism: Don’t know distributions Uncertainty

20. 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)

21. “Austrian” Economics • Uncertainty • Disequilibrium • Market as a process, not an end state

22. “If you cannot measure, your knowledge is meager and unsatisfactory.” Lord Kelvin

23. The Dilemma of the “Austrian” Actuary Your knowledge is meager and unsatisfactory, but you must make a recommendation.

24. Frank Knight, on the practical meaning of Kelvin’s statement for social scientists: “If you cannot measure, measure anyhow.”

25. Don’t ignore unmeasurables that bias results.

26. Measuring the Unmeasurable • Fraction of previous layer? • What would breach layer? • Capacity charge?