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Credibility Using Semiparametric Models

Published online by Cambridge University Press:  29 August 2014

Virginia R. Young
Virginia R. Young*
Affiliation:
School of Business, University of Wisconsin-Madison
*
School of Business, 975 University Avenue, University of Wisconsin-Madison, Madison, WI, USA53706
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Abstract

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To use Bayesian analysis to model 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. A criticism of this method is that the prior distribution can be difficult to choose and the resulting model may not represent the loss data very well. In this paper, we apply techniques from nonparametric density estimation to estimate the prior. We use the estimated model to calculate the predictive mean of future claims given past claims. We illustrate our method with simulated data from a mixture of a lognormal conditional over a lognormal prior and find that the estimated predictive mean is more accurate than the linear Bühlmann credibility estimator, even when we use a conditional that is not lognormal.

Keywords

Kernel density estimationclaim estimationBayesian estimation
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 27 , Issue 2 , November 1997 , pp. 273 - 285
Copyright
Copyright © International Actuarial Association 1997

References

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