IAI Actuarial Core Principles · Economic Modelling · Ruin theory
Individual claims to an Indian general insurer are exponential with mean Rs 50,000. The insurer takes excess of loss reinsurance with retention Rs 20,000 per claim. The expected retained claim amount per claim is closest to which value? (Use E[min(X,M)] = mean*(1-e^(-M/mean)); e^(-0.4)=0.6703)
The expected retained claim is about Rs 16,480, found as 50,000 times (1 minus e to the power minus 0.4). The figure of Rs 33,520 is the expected reinsured part, not the amount the insurer retains.
- ARs 16,480Correct
- BRs 20,000
- CRs 33,520
- DRs 13,406
- Rs 50,000
Explanation
Retained amount is min(X,20,000). E = 50,000*(1-e^(-0.4)) = 50,000*0.3297 = 16,485, about Rs 16,480. Rs 33,520 is the expected amount ceded (50,000*0.6703), the wrong side of the retention.
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