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

An insurer buys a quota share (proportional) reinsurance treaty under which it retains 70% of every claim. An individual claim X arises with E[X] = Rs 80,000 and Var(X) = Rs² 1,600,000,000. What is the standard deviation of the claim amount borne by the insurer after reinsurance?

The standard deviation is Rs 28,000. Under proportional reinsurance retaining 70%, the insurer's claim is 0.7X, so its standard deviation scales by 0.7. The original standard deviation is Rs 40,000, the square root of the variance, giving 0.7 × 40,000 = Rs 28,000.

  1. ARs 12,000
  2. BRs 20,000
  3. CRs 28,000Correct
  4. DRs 40,000
  5. Rs 56,000

Explanation

The insurer's claim is Y = 0.7X. SD(Y) = 0.7 × SD(X). SD(X) = sqrt(1,600,000,000) = 40,000, so SD(Y) = 0.7 × 40,000 = 28,000. Rs 20,000 wrongly multiplies by 0.5, and Rs 56,000 is the figure 0.7 × 80,000, the mean, not the SD.

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