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Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

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  • Boratyńska Agata

    (Warsaw School of Economics SGH, Collegium of Economic Analysis, Institute of Econometrics, Al. Niepodległości 162, 02-554 Warszawa, Poland .)

Abstract

The article presents a collective risk model for the insurance claims. The objective is to estimate a premium, which is defined as a functional specified up to unknown parameters. For this purpose, the Bayesian methodology, which combines the prior knowledge about certain unknown parameters with the knowledge in the form of a random sample, has been adopted. The generalised Bregman loss function is considered. In effect, the results can be applied to numerous loss functions, including the square-error, LINEX, weighted square-error, Brown, entropy loss. Some uncertainty about a prior is assumed by a distorted band class of priors. The range of collective and Bayes premiums is calculated and posterior regret Γ-minimax premium as a robust procedure has been implemented. Two examples are provided to illustrate the issues considered - the first one with an unknown parameter of the Poisson distribution, and the second one with unknown parameters of distributions of the number and severity of claims.

Suggested Citation

  • Boratyńska Agata, 2021. "Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 123-140, September.
    • Handle: RePEc:vrs:stintr:v:22:y:2021:i:3:p:123-140:n:8
    DOI: 10.21307/stattrans-2021-030
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    References listed on IDEAS

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