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arXiv · 1710.08553

Bayesian Credibility for GLMs

Oscar Alberto Quijano Xacur·José Garrido
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Abstract

We revisit the classical credibility results of Jewell and B\"uhlmann to obtain credibility premiums for a GLM using a modern Bayesian approach. Here the prior distributions 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.

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Oscar Alberto Quijano Xacur, José Garrido. 2017-10-23. Bayesian Credibility for GLMs. https://arxiv.org/abs/1710.08553

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