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

Published online by Cambridge University Press:  17 April 2015

Agata Boratyńska
Agata Boratyńska*
Affiliation:
Institute of Econometrics, Warsaw School of Economics, Al. Niepodległošci 162, 02-554 Warszawa, Poland, E-mail: aborata@sgh.waw.pl
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Abstract

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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.

Keywords

Bayesian modelclasses of priorsposterior regretsquare error lossLINEXinsurance premium
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 1 , May 2008 , pp. 277 - 291
Copyright
Copyright © ASTIN Bulletin 2008

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