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

For a compound Poisson aggregate loss S with Poisson parameter 3 and claim size X with E[X]=2000 and E[X^2]=6,000,000 (Rs squared), what is Var(S)?

For a compound Poisson distribution the variance of aggregate claims equals the Poisson parameter times the second moment of the claim size. Here that is 3 times 6,000,000, which is 18,000,000 Rs squared, not based on the claim variance.

  1. ARs squared 12,000,000
  2. BRs squared 18,000,000Correct
  3. CRs squared 6,000,000
  4. DRs squared 24,000,000
  5. Rs squared 30,000,000

Explanation

For compound Poisson, Var(S) = lambda E[X^2] = 3 x 6,000,000 = 18,000,000. Using lambda x Var(X) = 3 x 2,000,000 = 6,000,000 is the key error, since Var(X)=6,000,000-4,000,000=2,000,000.

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