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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

REFERENCES

Bowers, N. L.et al., (1986) Actuarial Mathematics. The Society of Actuaries, Itasca, Illinois.Google Scholar
De Pril, N. (1985) Recursions for convolutions of arithmetic distributions. ASTIN Bulletin 15, 135–139.CrossRefGoogle Scholar
De Pril, N. (1986) Moments of a class of compound distributions. Scand. Actuarial J. 1986, 117–120.CrossRefGoogle Scholar
Guldberg, A. (1931) On discontinuous frequency-functions and statistical series. Skandinavisk Aktuahetidskrift 14, 167–187.Google Scholar
Ord, J.K. (1967). On a system of discrete distributions. Biometrika 54, 649–656.Google ScholarPubMed
Panjer, H.H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 11, 22–26.CrossRefGoogle Scholar
Panjer, H. H. (1986) Direct calculation of ruin probabilities. The Journ. of Risk and Insurance LIII, 521–529.CrossRefGoogle Scholar
Panjer, H.H. and Willmot, G.E. (1982) Recursions for compound distributions. ASTIN Bulletin 13, 1–11.CrossRefGoogle Scholar
Panjer, H.H. and Willmot, G.E. (1986) Computational aspects of recursive evaluation of compound distributions. Insurance: Math. and Econ. 5, 113–116.Google Scholar
Schröter, K. J. (1990) On a family of counting distributions and recursions for related compound distributions. Scand. Actuarial J 1990, 161–174.CrossRefGoogle Scholar
Sundt, B. (1992) On some extensions of Panjer's class of counting distributions. ASTIN Bulletin 22, 61–80.CrossRefGoogle Scholar
Sundt, B. and Jewell, W. S. (1981) Further results on recursive evaluation of compound distributions. ASTIN Bulletin 11, 27–39.CrossRefGoogle Scholar
Willmot, G.E. and Panjer, H.H. (1987) Difference equation approaches in evaluation of compound distributions. Insurance: Math. and Econ. 6, 43–56.Google Scholar