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Document Details :

Title: Posterior Regret Γ-Minimax Estimation of Insurance Premium in Collective Risk Model
Author(s): BORATYŃSKA, Agata
Journal: ASTIN Bulletin
Volume: 38    Issue: 1   Date: May 2008   
Pages: 277-291
DOI: 10.2143/AST.38.1.2030414

Abstract :
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 θ (the expected number of claims). Four principles of calculating a premium are applied. The Bayesian methodology, which combines the prior knowledge about a parameter θ 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 Γ-minimax premiums are calculated, as an optimal robust premiums. A numerical example is presented.