IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
Aggregate claims S = X1 + ... + XN, where N is Poisson with mean 20 and the Xi are independent and identically distributed with mean Rs 5,000 and variance 4,000,000 (Rs squared), independent of N. What is E[S]?
The expected aggregate claim is Rs 1,00,000. For any compound distribution with independent claim number and sizes, the mean equals the expected number of claims times the mean claim size, so 20 multiplied by Rs 5,000 gives Rs 1,00,000.
- ARs 25,000
- BRs 1,00,000Correct
- CRs 20,000
- DRs 1,05,000
- Rs 5,000
Explanation
E[S] = E[N]E[X] = 20 x 5,000 = Rs 1,00,000. Rs 25,000 is wrong because it adds 20 and 5,000 or uses the wrong scale, and Rs 20,000 ignores the claim mean.
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