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IAI Actuarial Core Principles · Economic Modelling · Role of insurance in reducing or removing risk

An Indian general insurer buys a quota share reinsurance treaty ceding 30% of every policy in a motor portfolio. Which statement about the effect on the insurer's claims experience is correct?

Quota share scales every claim by the retained proportion, so mean and standard deviation both fall by 30%. The coefficient of variation therefore stays the same. Relative riskiness is unchanged, although the absolute exposure of the insurer is lower.

  1. AEach claim is reduced by 30% for the insurer, so the coefficient of variation of its retained claims is unchangedCorrect
  2. BThe insurer's variance of retained claims is reduced by 30% but its mean is unchanged
  3. CThe insurer retains only claims above a fixed monetary limit
  4. DThe insurer's largest single claim is unchanged because quota share applies only to the aggregate
  5. The insurer's retained claims become fully deterministic

Explanation

Under a quota share the retained claim is 0.7X. The mean falls to 0.7E[X] and the standard deviation to 0.7 sd(X), so the coefficient of variation is unchanged. The variance falls by 51%, not 30%. Quota share does not reduce the relative variability, whereas excess of loss changes the shape of the distribution.

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