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

When approximating a continuous claim severity distribution by a discrete one in order to apply Panjer recursion, the method of rounding with span h places mass at multiples of h. Which statement about this approach is correct?

Reducing the span h improves the accuracy of the discretised severity, but it increases the number of recursion steps required to cover the same range of aggregate claims. A coarse span is quicker but less accurate, and the span need not equal the mean.

  1. AReducing the span h increases accuracy but increases the number of recursion steps needed to reach a given aggregate amountCorrect
  2. BA larger span always gives a more accurate answer because fewer terms are summed
  3. CThe method cannot preserve the mean of the severity distribution under any choice of span
  4. DRounding approximations are valid only for Poisson claim numbers with integer mean
  5. The span must equal the mean claim amount for the recursion to be valid

Explanation

A smaller span discretises the severity more finely, reducing approximation error, but to cover the same range of aggregate claims you need more steps. A larger span is coarser and less accurate, and there is no requirement that h equal the mean.

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