IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
Annual claim numbers N follow a Poisson distribution with mean 4, and individual claim amounts X are i.i.d. with mean Rs 25,000 and variance 100,000,000 (Rs squared), independent of N. What is the expected value of aggregate annual claims S?
The expected aggregate claims equal the expected number of claims times the mean claim size, which is 4 multiplied by Rs 25,000, giving Rs 100,000. The claim size variance is not needed for the mean of a compound distribution.
- ARs 25,000
- BRs 62,500
- CRs 100,000Correct
- DRs 125,000
- Rs 400,000
Explanation
E[S] = E[N]E[X] = 4 x 25,000 = Rs 100,000. Rs 25,000 ignores the claim frequency. Rs 400,000 wrongly uses E[N] x E[X^2]-type reasoning or the variance scale, and is not the mean.
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