IAI Actuarial Core Principles · Economic Modelling · Ruin theory
An insurer's surplus follows a compound Poisson model with claim size distribution exponential with mean 1,000 (rupees) and premium loading theta over the expected claims. With proportional reinsurance, the insurer keeps a fraction alpha of every claim and pays the reinsurer a premium that includes a higher loading than the insurer's own. Which statement about the effect on the insurer's adjustment coefficient is correct in general?
The adjustment coefficient can increase after proportional reinsurance because retained claims are less variable, even though the insurer gives up some premium margin. Whether it rises depends on the loadings and the retention, so it does not always rise or fall.
- AReinsurance always increases the adjustment coefficient, whatever the reinsurer's loading
- BThe adjustment coefficient can rise because claim variability falls, even though retained premium income per unit time is lowerCorrect
- CReinsurance has no effect on the adjustment coefficient because the claim frequency is unchanged
- DThe adjustment coefficient falls whenever alpha is below 1 because the ruin probability must rise
- The adjustment coefficient is unaffected by claim size distribution once reinsurance is bought
Explanation
Proportional reinsurance reduces the retained claim variability, which tends to raise R, but the net premium retained is reduced by the reinsurer's loading. The net effect depends on the loadings and alpha, so it can increase R. The claim that R always rises ignores the reinsurer's expensive loading.
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