On Bayesian mixture credibility

John W. Lau, Tak Kuen Siu, Hailiang Yang

Research output: Contribution to journalArticle

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. © 2006 by Astin Bulletin. All rights reserved.

Original languageEnglish
Pages (from-to)573-588
Number of pages16
JournalASTIN Bulletin: The Journal of the IAA
Volume36
Issue number2
DOIs
Publication statusPublished - Nov 2006

Keywords

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

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