Bayesian credibility premium with GB2 copulas

For observations over a period of time, Bayesian credibility premium may be used to predict the value of a response variable for a subject, given previously observed values. In this article, we formulate Bayesian credibility premium 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 credibility premium. Numerical illustrations show the application of these estimators in determining experience-rated insurance premium. We consider generalized Pareto as a special case.

Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces

We shall study some connection between averaging operators and martingale inequalities in rearrangement invariant function spaces. In Section 2 the equivalence between Shimogaki’s theorem and some martingale inequalities will be established, and in Section 3 the equivalence between Boyd’s theorem andmartingale inequalities with change of probability measure will be established.