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

Boratyńska Agata ()
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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 .

Statistics in Transition New Series, 2021, vol. 22, issue 3, 123-140

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.

Keywords: classes of priors; posterior regret; distortion function; Bregman loss; insurance premium (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:stintr:v:22:y:2021:i:3:p:123-140:n:8

DOI: 10.21307/stattrans-2021-030

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