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On Multivariate Panjer Recursions

Published online by Cambridge University Press:  29 August 2014

Bjørn Sundt
Bjørn Sundt*
Affiliation:
University of Bergen & University of Melbourne
*
Department of Mathematics, University of Bergen, Johannes Bruns gate 12, N-5008 Bergen, Norway
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Abstract

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In the present paper we generalise Panjer's (1981) recursion for compound distributions to a multivariate situation where each claim event generates a random vector. We discuss situations within insurance where such models could be applicable, and consider some special cases of the general algorithm. Finally we deduce from the algorithm a multivariate extension of De Pril's (1985) recursion for convolutions.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 1 , May 1999 , pp. 29 - 45
Copyright
Copyright © International Actuarial Association 1999

References

De Pril, N. (1985). Recursions for convolutions of arithmetic distributions. ASTIN Bulletin 15, 135–139.Google Scholar
Hesselager, O. (1996). Recursions for certain bivariate counting distributions and their compound distributions. ASTIN Bulletin 26, 35–52.Google Scholar
Panjer, H.H. (1981). Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 22–26.Google Scholar
Sundt, B. (1992). On some extensions of Panjer's class of counting distributions. ASTIN Bulletin 22, 61–80.CrossRefGoogle Scholar
Sundt, B. (1993). An introduction to non-life insurance mathematics. (3. ed.) Verlag Versicherungswirtschaft e.V., Karlsruhe.Google Scholar
Sundt, B. (1998). The multivariate De Pril transform. Research paper 59, Centre for Actuarial Studies, University of Melbourne.Google Scholar