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An Extension of Panjer's Recursion

Published online by Cambridge University Press:  29 August 2014

Klaus Th. Hess ,
Anett Liewald  and
Klaus D. Schmidt
Klaus Th. Hess*
Affiliation:
Lehrstuhl für Versicherungsmathematik, Technische Universität Dresden
Anett Liewald*
Affiliation:
Lehrstuhl für Versicherungsmathematik, Technische Universität Dresden
Klaus D. Schmidt*
Affiliation:
Lehrstuhl für Versicherungsmathematik, Technische Universität Dresden
*
Lehrstuhl für Versicherungsmathemetik, Technische Universität Dresden, D-01062 Dresden E-mail:[email protected]
Lehrstuhl für Versicherungsmathemetik, Technische Universität Dresden, D-01062 Dresden E-mail:[email protected]
Lehrstuhl für Versicherungsmathemetik, Technische Universität Dresden, D-01062 Dresden E-mail:[email protected]
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Abstract

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Sundt and Jewell have shown that a nondegenerate claim number distribution Q = {qn}nϵN0 satisfies the recursion

for all n≥0 if and only if Q is a binomial, Poisson or negativebinomial distribution. This recursion is of interest since it yields a recursion for the aggregate claims distribution in the collective model of risk theory when the claim size distribution is integer-valued as well. A similar characterization of claim number distributions satisfying the above recursion for all n ≥ 1 has been obtained by Willmot. In the present paper we extend these results and the subsequent recursion for the aggregate claims distribution to the case where the recursion holds for all n ≥ k with arbitrary k. Our results are of interest in catastrophe excess-of-loss reinsurance.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 32 , Issue 2 , November 2002 , pp. 283 - 297
Copyright
Copyright © International Actuarial Association 2002

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