Credibility premiums for natural exponential family and general 0-1 loss function

Abstract

In credibility theory, the premium charged to a policyholder is computed on the basis of his past claims and the accumulated past claims of the corresponding portfolio of policyholders. In order to obtain an appropriate expression for this quantity, different approaches within Bayesian statistical decision theory, such as empirical Bayes, gamma minimax and posterior regret gamma minimax estimation have been proposed in the actuarial literature. This paper introduces a new parametric family of Bayesian estimators into the methodology of premium calculation principles. This is achieved by using a general class of 0-1 loss function when the natural exponential family of distribution is used. Consequently, new credibility expressions are obtained.