A Recursive Procedure for Calculation of some Compound Distributions

Ole Hesselager

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Probability and Risk Models Probability and Statistical Research Statistical Distribution Estimation and Applications

Abstract

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.

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References

1981Recursive Evaluation of a Family of Compound Distributions 1981Further Results on Recursive Evaluation of Compound Distributions 1986Actuarial Mathematics 1992On some Extensions of Panjer's Class of Counting Distributions 1985Recursions for Convolutions of Arithmetic Distributions 1986Direct Calculation of Ruin Probabilities 1987Difference equation approaches in evaluation of compound distributions 1986Computational aspects of recursive evaluation of compound distributions

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