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A Class of Conjugate Priors with Applications to Excess-of-Loss Reinsurance

Published online by Cambridge University Press:  29 August 2014

Ole Hesselager
Ole Hesselager*
Affiliation:
University of Copenhagen, Denmark
*
Laboratory of Actuarial Mathematics, Universitetsparken 5, University of Copenhagen, DK-2100 Copenhagen Ø.
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Abstract

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We consider the problem of forecasting the total cost of claims in excess-of-loss reinsurance. The number of claims reported to the direct insurer is assumed to follow a Poisson law, and the claim severities are modelled by a Pareto distribution. The Poisson frequency as well as the Pareto parameter will be considered as random parameters in a Bayesian setting. We derive the class of conjugate joint prior distributions, which turn out to specify a (prior) dependence between the two parameters. The use of conjugate priors facilitates the mathematical analysis, and it also makes it easy to interpret the parameters of the prior distribution.

Keywords

Excess-of-loss quotationslimited coverPareto distributionconjugate priors
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 23 , Issue 1 , May 1993 , pp. 77 - 93
Copyright
Copyright © International Actuarial Association 1993

References

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