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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 q (the expected number of claims). Four principles of calculating a premium are applied. The Bayesian methodology, which combines the prior knowledge about a parameter q 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 G-minimax premiums are calculated, as an optimal robust premiums. A numerical example is presented. KEYWORDSBayesian model, classes of priors, posterior regret, square error loss, LINEX, insurance premium.

The problem of robust Bayesian estimation in some models with an asymmetric loss function (LINEX) is considered. Some uncertainty about the prior is assumed by introducing two classes of priors. The most robust and conditional Γ -minimax estimators are constructed. The situations when those estimators coincide are presented.

Abstract. The problem of posterior regret Γ -minimax estimation under LINEX loss function is considered. A general form of posterior regret Γ -minimax estimators is presented and it is applied to a normal model with two classes of priors. A situation when the posterior regret Γ -minimax estimator, the most stable estimator and the conditional Γ -minimax estimator coincide is presented.

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