Posterior Regret G-Minimax Estimation of Insurance Premium in Collective Risk Model

The collective risk model for the insurance claims is considered. The objective is to estimate a premium which is defined as a functional H specified up to an unknown parameter ? (the expected number of claims). Four principles of calculating a premium are applied. The Bayesian methodology, which combines the prior knowledge about a parameter ? with the knowledge in the form of a random sample is adopted. Two loss functions (the square-error loss function and the asymmetric loss function LINEX) are considered. Some uncertainty about a prior is assumed by introducing classes of priors. Considering one of the concepts of robust procedures the posterior regret ?-minimax premiums are calculated, as an optimal robust premiums. A numerical example is presented.

Keywords: Bayesian model, classes of priors, posterior regret, square error loss, LINEX, insurance premium.