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

In the collective risk model S = X1 + X2 + ... + XN, which of the following is a required assumption for the standard compound distribution results?

The standard collective risk model assumes claim sizes are independent and identically distributed and independent of the claim number N. No particular distribution is required for either component, and dependence between claim sizes and the number of claims would invalidate the usual mean and variance formulae.

  1. AThe claim sizes X_i are independent and identically distributed, independent of the claim number NCorrect
  2. BThe claim sizes must be exponentially distributed
  3. CThe claim number N must be Poisson distributed
  4. DThe claim sizes must be positively correlated with N
  5. The claim sizes must have a mean equal to the variance of N

Explanation

The standard collective risk model requires the claim amounts to be iid and independent of the number of claims N. No specific distribution is needed for N or X, so the Poisson and exponential options are too restrictive, and correlation between X and N would break the usual formulae.

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