Some Bayesian credibility premiums obtained by using posterior regret {$\Gamma$}-minimax methodology

Abstract

In credibility theory, the premium charged to a policyholder is computed on the basis of his/her own past claims and the accumulated past claims of the corresponding portfolio of policyholders. In order to obtain an appropriate formula for this, various methodologies have been proposed in actuarial literature, most of them in the field of Bayesian decision methodology.

In this paper, following the robust Bayesian paradigm, a procedure based on the posterior regret $\Gamma$-minimax principle is applied to derive, in a straightforward way, new credibility formula, making use of simple classes of distributions. This methodology is applied to the most commonly used premium calculation principles in insurance, namely the net, Esscher and variance principles.