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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Loss distributions, with and without risk sharing

Claim amounts X are uniformly distributed on (0, 100,000) rupees. An excess of loss treaty has retention Rs 60,000 with no upper limit. What is the expected payment by the reinsurer per claim (including claims that cause no reinsurance payment)?

The reinsurer's expected payment per claim is Rs 8,000. It equals the integral of (x - 60,000)/100,000 from 60,000 to 100,000, which is 40,000² / (2 × 100,000). The figure of Rs 20,000 is only the average given that the retention is exceeded.

  1. ARs 4,000
  2. BRs 8,000Correct
  3. CRs 12,000
  4. DRs 20,000
  5. Rs 40,000

Explanation

Reinsurer pays (X - 60,000) when X exceeds 60,000. E = integral from 60,000 to 100,000 of (x - 60,000)/100,000 dx = (1/100,000) × 40,000²/2 = 800,000,000/100,000 = 8,000. Rs 20,000 is the conditional mean given the claim exceeds the retention, and ignores the 40% probability weighting.

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