Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-28T14:40:13.126Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  29 August 2014

Ole Hesselager*
Affiliation:
University of Copenhagen, Denmark
*
Laboratory of Actuarial Mathematics, Universitetsparken 5, University of Copenhagen, DK-2100 Copenhagen Ø.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Articles
Copyright
Copyright © International Actuarial Association 1993

References

REFERENCES

Goovaerts, M.J., de Vylder, F. and Haezendonck, J. ( 1984) Insurance premiums. North-Holland, Amsterdam-New York.Google Scholar
Hartigan, J.A. (1983) Bayes theory. Springer-Verlag, New York.CrossRefGoogle Scholar
Jewell, W.S. (1990) Up the misty staircase with credibility theory. Mitteil. Schweiz. Verein. Versich. Math., 90, 281312.Google Scholar
Jewell, W.S. (1991) The value of information in forcasting excess losses. Paper presented to the 23rd Astin Colloquium, Stockholm.Google Scholar
Patrik, G. and Mashitz, I. (1989) Credibility for reinsurance excess pricing. Paper presented at the 21st Astin Colloquium, New York.Google Scholar
Panjer, H.H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 11, 2226.CrossRefGoogle Scholar
Rytgaard, M. (1990) Estimation in the Pareto distribution. ASTIN Bulletin 20, 201216.CrossRefGoogle Scholar