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A Recursive Procedure for Calculation of some Compound Distributions

Published online by Cambridge University Press:  29 August 2014

Ole Hesselager
Ole Hesselager*
Affiliation:
University of Copenhagen
*
Laboratory of Actuarial Mathematics, Universiteitsparken 5, University of Copenhagen, DK-2100 Copenhagen Ø.
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Abstract

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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.

Keywords

Recursionscompound distributionsmomentsprobablity of ruin
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 1 , May 1994 , pp. 19 - 32
Copyright
Copyright © International Actuarial Association 1994

References

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