IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing
A health insurer's claim X is uniform on (0, 100,000). Under a policy with an ordinary deductible of Rs 30,000, what is the expected payment per payment (given that a payment is made)?
The expected payment per payment is Rs 35,000. Given the loss exceeds the deductible, it is uniform between 30,000 and 100,000 with mean 65,000, and subtracting the deductible of 30,000 gives 35,000.
- ARs 35,000Correct
- BRs 30,000
- CRs 70,000
- DRs 49,000
- Rs 40,000
Explanation
Given X > 30,000, X is uniform on (30,000, 100,000), so its mean is 65,000. The payment is X − 30,000, with mean 35,000. Rs 49,000 is the per-loss expectation 0.7 × 35,000 = 24,500 doubled mistakenly; Rs 24,500 would be the per-loss figure, not per payment.
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