A Recursive Procedure for Calculation of some Compound Distributions
Open Access
- 1 May 1994
- journal article
- Published by Cambridge University Press (CUP) in ASTIN Bulletin
- Vol. 24 (1) , 19-32
- https://doi.org/10.2143/ast.24.1.2005078
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.Keywords
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