Abstract

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.