IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
The number of claims N on a motor portfolio is Poisson with mean 20 per year. Claim sizes are independent with mean ₹5,000 and variance 4,000,000 (₹²). What is the variance of annual aggregate claims, in ₹²?
The variance is 580,000,000 ₹². Using Var(S) = E[N]Var(X) + Var(N)E[X]², the first term is 20×4,000,000 = 80 million and the second is 20×25 million = 500 million, which sum to 580 million.
- A580,000,000Correct
- B500,000,000
- C100,000,000
- D80,000,000
- 20,000,000
Explanation
Var(S) = E[N]Var(X) + Var(N)E[X]². For Poisson, Var(N)=20. So 20×4,000,000 = 80,000,000 and 20×25,000,000 = 500,000,000. Total = 580,000,000. Using only the second term (500,000,000) omits the claim size variability.
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