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Document Details : Title: On Bayesian Mixture Credibility Author(s): LAU, John W. , SIU, Tak Kuen , YANG, Hailiang Journal: ASTIN Bulletin Volume: 36 Issue: 2 Date: 2006 Pages: 573-588 DOI: 10.2143/AST.36.2.2017934 Abstract : 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. |
