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June 2009 Some Bayesian credibility premiums obtained by using posterior regret {$\Gamma$}-minimax methodology
E. Gómez-Déniz
Bayesian Anal. 4(2): 223-242 (June 2009). DOI: 10.1214/09-BA408

Abstract

In credibility theory, the premium charged to a policyholder is computed on the basis of his/her own past claims and the accumulated past claims of the corresponding portfolio of policyholders. In order to obtain an appropriate formula for this, various methodologies have been proposed in actuarial literature, most of them in the field of Bayesian decision methodology.

In this paper, following the robust Bayesian paradigm, a procedure based on the posterior regret $\Gamma$-minimax principle is applied to derive, in a straightforward way, new credibility formula, making use of simple classes of distributions. This methodology is applied to the most commonly used premium calculation principles in insurance, namely the net, Esscher and variance principles.

Citation

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E. Gómez-Déniz. "Some Bayesian credibility premiums obtained by using posterior regret {$\Gamma$}-minimax methodology." Bayesian Anal. 4 (2) 223 - 242, June 2009. https://doi.org/10.1214/09-BA408

Information

Published: June 2009
First available in Project Euclid: 22 June 2012

zbMATH: 1330.62124
MathSciNet: MR2507362
Digital Object Identifier: 10.1214/09-BA408

Rights: Copyright © 2009 International Society for Bayesian Analysis

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Vol.4 • No. 2 • June 2009
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