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On Bayesian Mixture Credibility

Published online by Cambridge University Press:  17 April 2015

John W. Lau ,
Tak Kuen Siu  and
Hailiang Yang
John W. Lau
Affiliation:
Department of Mathematics, University of Bristol, Bristol, United Kingdom, Email: John.Lau@bristol.ac.uk
Tak Kuen Siu
Affiliation:
Department of Actuarial, Mathematics and Statistics School of Mathematical and Computer Sciences and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, United Kingdom, E-mail: T.K.Siu@ma.hw.ac.uk
Hailiang Yang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, Email: hlyang@hkusua.hku.hk
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Abstract

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We introduce a class of Bayesian infinite mixture models first introduced by Lo (1984) to determine the credibility premium for a non-homogeneous insurance portfolio. The Bayesian infinite mixture models provide us with much flexibility in the specification of the claim distribution. We employ the sampling scheme based on a weighted Chinese restaurant process introduced in Lo et al. (1996) to estimate a Bayesian infinite mixture model from the claim data. The Bayesian sampling scheme also provides a systematic way to cluster the claim data. This can provide some insights into the risk characteristics of the policyholders. The estimated credibility premium from the Bayesian infinite mixture model can be written as a linear combination of the prior estimate and the sample mean of the claim data. Estimation results for the Bayesian mixture credibility premiums will be presented.

Keywords

Credibility TheoryBayesian Mixture ModelsInfinite MixtureRisk CharacteristicsClusteringWeighted Chinese Restaurant ProcessCredibility Premium PrincipleDirichlet Process
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 2 , November 2006 , pp. 573 - 588
Copyright
Copyright © ASTIN Bulletin 2006

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