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The True Claim Amount and Frequency Distributions within a Bonus-Malus System

Published online by Cambridge University Press:  29 August 2014

Jean François Walhin  and
José Paris
Jean François Walhin*
Affiliation:
Université Catholique de Louvain Secura Belgian Re
José Paris*
Affiliation:
Université Catholique de Louvain
*
Institut de Statistique, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium, E-mail:walhin@stat.ucl.ac.be
Institut de Statistique, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium, E-mail:walhin@stat.ucl.ac.be
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Abstract

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We apply Lemaire's algorithm and a non-parametric mixed Poisson fit to a motor insurance portfolio in order to find the true claim frequency and claim amount distributions. The algorithm we develop accounts for the fact that observed distributions are distorted by bonus hunger, when a bonus-malus system is used by the insurer.

Keywords

Mixed Poisson distributionnon-parametric fitbonus-malus systemhunger for bonusclaim amount distributionfrequency distributioncensoringmaximum likelihood
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 30 , Issue 2 , November 2000 , pp. 391 - 403
Copyright
Copyright © International Actuarial Association 2000

References

Lemaire, J. (1977) La Soif du Bonus. ASTIN Bulletin 9, 181–190.CrossRefGoogle Scholar
Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Kluwer, Boston.CrossRefGoogle Scholar
Walhin, J.F. and Paris, J. (1999) Using Mixed Poisson Distributions in Connection with Bonus-Malus Systems. ASTIN Bulletin 29, 81–99.CrossRefGoogle Scholar