Bayesian ratemaking with common effects modeled by mixture of Polya tree processes

In classical models for Bayesian ratemaking, claims are usually assumed to be independent over risks. However, this assumption may be violated because there are situations that could derive possible dependence among the insured individuals. This paper aims to investigate the typical problem of experience ratemaking to account for a special type of dependence that is known as common effects in the literature. Polya tree processes are employed to model the common effects and, by means of an MCMC scheme, the corresponding Bayesian premiums are numerically computed. This provides a useful alternative to the well known results on Bayesian ratemaking with common effects.