Bayesian Credibility for GLMs

10/23/2017

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by   Oscar Alberto Quijano Xacur, et al.

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We revisit the classical credibility results of Jewell and Bühlmann to obtain credibility premiums for a GLM severity model using a modern Bayesian approach. Here the prior distributions are chosen from out-of-sample information, without restrictions to be conjugate to the severity distribution. Then we use the relative entropy between the "true" and the estimated models as a loss function, without restricting credibility pre miums 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.