levels of determinism in workers’ compensation reinsurance commutations [pcas 1999] gary blumsohn...

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


Levels of Determinism

No determinism:Don’t know distributions


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







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


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


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







Method 1Method 1

Method 2Method 2

Method 3Method 3

Next step:Judgmental leap

Next step:Judgmental leap



Economic Perspective on Levels of Determinism





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?

levels of determinism in workers’ compensation reinsurance commutations [pcas 1999] gary blumsohn...

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