We revisit the classical credibility results of Jewell (1974) and Bühlmann (1967) to obtain credibility premiums for a GLM using a modern Bayesian approach. Here the prior distribution can be chosen without restrictions to be conjugate to the response distribution. It can even come from out–of–sample information if the actuary prefers.
Then we use the relative entropy between the “true” and the estimated models as a loss function, without restricting credibility premiums to be linear. A numerical illustration on real data shows the feasibility of the approach, now that computing power is cheap, and simulations software readily available.