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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
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.