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1 results

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

  • Agata Boratyńska
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 38 / Issue 1 / May 2008
    Published online by Cambridge University Press:
    17 April 2015, pp. 277-291
    Print publication:
    May 2008
    • Article
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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 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.