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A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component

Published online by Cambridge University Press:  07 February 2018

Georges Dionne  and
Charles Vanasse
Georges Dionne*
Affiliation:
Université de Montréal, Canada
Charles Vanasse*
Affiliation:
Université de Montréal, Canada
*
CRT, Université de Montréal, C.P. 6128, Succ. A, Montreal, H3C 3J7, Canada
CRT, Université de Montréal, C.P. 6128, Succ. A, Montreal, H3C 3J7, Canada
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Abstract

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The objective of this paper is to provide an extension of well-known models of tarification in automobile insurance. The analysis begins by introducing a regression component in the Poisson model in order to use all available information in the estimation of the distribution. In a second step, a random variable is included in the regression component of the Poisson model and a negative binomial model with a regression component is derived. We then present our main contribution by proposing a bonus-malus system which integrates a priori and a posteriori information on an individual basis. We show how net premium tables can be derived from the model. Examples of tables are presented.

Keywords

Multivariate automobile insurance ratingPoisson modelnegative binomial modelregression componentnet premium tablesBayes analysismaximum likelihood method
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 19 , Issue 2 , November 1989 , pp. 199 - 212
Copyright
Copyright © International Actuarial Association 1989

Footnotes

*

Centre de recherche sur les transports and Department of Economics. This research was financed by SSHRC Canada. Comments on a previous version of the paper by Alois Gisler, Christian Gourieroux, Stuart Klugman, Jean Lemaire, David Scott and two anonymous referees were very useful.

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