Computational Bayesian Methods for Insurance Premium Estimation

Bayesian Inference is used to develop a credibility estimator and a method to compute insurance premium risk loadings. Algorithms to apply both methods to Generalized Linear Models (GLMs) are provided. We call our credibility estimator the entropic premium. It is a Bayesian point estimator that uses the relative entropy as the loss function. The risk measures Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR) are used to determine premium risk loadings. Our method considers the number of insureds and their durations as random variables. A distribution to model the duration of risks is introduced. We call it unifed, it has support on the interval (0,1), it is an exponential dispersion family and it can be used as the response distribution of a GLM.