On Bayesian mixture credibility

John W. Lau*, Tak Kuen Siu, Hailiang Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)573-588
Number of pages16
JournalASTIN Bulletin
Issue number2
Publication statusPublished - Nov 2006
Externally publishedYes


  • Bayesian mixture models
  • Clustering
  • Credibility premium principle
  • Credibility theory
  • Dirichlet process
  • Infinite mixture
  • Risk characteristics
  • Weighted Chinese Restaurant process


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