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Keywords:

  • Bayesian nonparametric analysis;
  • compound Poisson process;
  • exchangeable claim process;
  • exchangeable sequence;
  • panel data;
  • risk model

Abstract

When dealing with risk models the typical assumption of independence among claim size distributions is not always satisfied. Here we consider the case when the claim sizes are exchangeable and study the implications when constructing aggregated claims through compound Poisson-type processes. In particular, exchangeability is achieved through conditional independence, using parametric and nonparametric measures for the conditioning distribution. Bayes' theorem is employed to ensure an arbitrary but fixed marginal distribution for the claim sizes. A full Bayesian analysis of the proposed model is illustrated with a panel-type data set coming from a Medical Expenditure Panel Survey (MEPS). Copyright © 2009 John Wiley & Sons, Ltd.