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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling

The number of claims N on a Mumbai motor portfolio is Poisson with mean 20. Individual claim amounts have mean ₹5,000 and standard deviation ₹3,000, and are independent of N. What is the variance of aggregate claims S?

The variance is ₹680 million. For a compound Poisson distribution, Var(S) = λE[X²], where E[X²] = 3,000² + 5,000² = 34 million. Multiplying by λ = 20 gives 680 million. Using only the claim size variance would understate the variability.

  1. A₹180 million
  2. B₹500 million
  3. C₹900 million
  4. D₹680 millionCorrect
  5. ₹1,000 million

Explanation

For Poisson N, Var(S) = λE[X²]. E[X²] = 3,000² + 5,000² = 9,000,000 + 25,000,000 = 34,000,000. Then Var(S) = 20 × 34,000,000 = 680,000,000, i.e. ₹680 million. Using only the variance of X gives 180 million, which is wrong because it ignores the variability from the claim number.

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