Bayesian Credibility Premium with GB2 Copulas

Bayesian shrinkage estimation is a familiar concept that arises from minimizing the Bayes risk under the squared error loss. For observations over a period of time, Bayesian shrinkage estimators may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate such estimators under a change of probability measure within the copula framework. Such reformulation is demonstrated using the multivariate generalized beta of the second kind (GB2) distribution. Within this family of GB2 copulas, we are able to derive explicit form of Bayesian shrinkage estimators. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case