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Robust Bayesian Credibility Using Semiparametric Models

Published online by Cambridge University Press:  29 August 2014

Virginia R. Young
Virginia R. Young*
Affiliation:
University of Wisconsin– Madison
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Abstract

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In performing Bayesian analysis of insurance losses, one usually chooses a parametric conditional loss distribution for each risk and a parametric prior distribution to describe how the conditional distributions vary across the risks. Young (1997) applies techniques from nonparametric density estimation to estimate the prior and uses the estimated model to calculate the predictive mean of future claims given past claims. A shortcoming of this method is that, in estimating the prior, one assumes the average claim amount equals the conditional claim. In this paper, we consider a class of priors obtained by perturbing the one determined nonparametrically, as in Young (1997). We thereby reflect the uncertainty in the prior that arises from the randomness in the claim data. We, then, calculate intervals for the corresponding predictive means. We illustrate our method with data from Dannenburg et al. (1996) and compare the intervals of the predictive means with nonparametric confidence intervals.

Keywords

Kernel density estimationclaim estimationrobust Bayesian estimationDempster-Shafer belief functionsupper and lower expectations
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 28 , Issue 2 , November 1998 , pp. 187 - 203
Copyright
Copyright © International Actuarial Association 1998

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