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Modified Recursions for a Class of Compound Distributions

Published online by Cambridge University Press:  29 August 2014

Karl-Heinz Waldmann
Karl-Heinz Waldmann*
Affiliation:
Inst. f. Wirtschaftstheorie und Operations Research, Universität Karlsruhe, D-76128, Karlsruhe
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Abstract

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Recursions are derived for a class of compound distributions having a claim frequency distribution of the well known (a,b)-type. The probability mass function on which the recursions are usually based is replaced by the distribution function in order to obtain increasing iterates. A monotone transformation is suggested to avoid an underflow in the initial stages of the iteration. The faster increase of the transformed iterates is diminished by use of a scaling function. Further, an adaptive weighting depending on the initial value and the increase of the iterates is derived. It enables us to manage an arbitrary large portfolio. Some numerical results are displayed demonstrating the efficiency of the different methods. The computation of the stop-loss premiums using these methods are indicated. Finally, related iteration schemes based on the cumulative distribution function are outlined.

Keywords

Collective risk modelaggregate claims distributionPanjer's algorithm
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 2 , November 1996 , pp. 213 - 224
Copyright
Copyright © International Actuarial Association 1996

References

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