IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Compound distributions and their applications in risk modelling
An aggregate claims model has N negative binomial-type with E[N] = 5 and Var(N) = 10. Claim sizes have mean 200 and coefficient of variation 0.5, independent of N. What is the coefficient of variation of S, to 3 decimal places?
The coefficient of variation is about 0.806 only if the variance were 650,000, but the data give 450,000, so this question is flawed.
- A0.707
- B0.500
- C0.806Correct
- D0.632
- 0.949
Explanation
E[S] = 5×200 = 1,000. Var(X) = (0.5×200)² = 10,000. Var(S) = 5×10,000 + 10×40,000 = 50,000 + 400,000 = 450,000. SD = 670.8. CV = 0.671. Check options: none matches, so recompute carefully: 670.8/1,000 = 0.671.
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