A Recursive Procedure for Calculation of some Compound Distributions

Ole Hesselager

ASTIN Bulletin, 1994, vol. 24, issue 1, 19-32

Abstract: We consider compound distributions where the counting distribution has the property that the ratio between successive probabilities may be written as the ratio of two polynomials. We derive a recursive algorithm for the compound distribution, which is more efficient than the one suggested by Panjer & Willmot (1982) and Willmot & Panjer (1987). We also derive a recursive algorithm for the moments of the compound distribution. Finally, we present an application of the recursion to the problem of calculating the probability of ruin in a particular mixed Poisson process.

Date: 1994
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