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Heavy-Tailed Distributions and Rating

Published online by Cambridge University Press:  29 August 2014

J. Beirlant ,
G. Matthys  and
G. Dierckx
J. Beirlant
Affiliation:
University Center of Statistics, Katholieke Universiteit Leuven
G. Matthys
Affiliation:
University Center of Statistics, Katholieke Universiteit Leuven
G. Dierckx
Affiliation:
University Center of Statistics, Katholieke Universiteit Leuven
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Abstract

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In this paper we consider the problem raised in the Astin Bulletin (1999) by Prof. Benktander at the occasion of his 80th birthday concerning the choice of an appropriate claim size distribution in connection with reinsurance rating problems. Appropriate models for large claim distributions play a central role in this matter. We review the literature on extreme value methodology and consider its use in reinsurance. Whereas the models in extreme-value methods are non-parametric or semi-parametric of nature, practitioners often need a fully parametric model for assessing a portfolio risk both in the tails and in more central portions of the claim distribution. To this end we propose a parametric model, termed the generalised Burr-gamma distribution, which possesses such flexibility. Throughout we consider a Norwegian fire insurance portfolio data set in order to illustrate the concepts. A small sample simulation study is performed to validate the different methods for estimating excess-of-loss reinsurance premiums.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 1 , May 2001 , pp. 37 - 58
Copyright
Copyright © International Actuarial Association 2001

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