On bivariate credibility estimator with GLM theory

Abstract

Credibility theory is one of the cornerstones of actuarial science as applied to casualty and property insurance, based on the concept of limiting the estimator of individual premium to the class of estimators that are linear with respect to all observations of the portfolio. This work deals with the bivariate data(number and amounts of claims of the contracts), we give the bivariate credibility estimator using exponential families and GLM theory. Just like in the case of classical credibility model we will obtain a credible solution in the form of a linear combination of the individual estimate and the collective estimate. And we add the proprieties on exact Bayes premium.