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The Practical Replacement of a Bonus-Malus System

Published online by Cambridge University Press:  29 August 2014

J.F. Walhin  and
J. Paris
J.F. Walhin*
Affiliation:
Université Catholique de Louvain Secura Belgian Re
J. Paris*
Affiliation:
Université Catholique de Louvain
*
Secura Belgian Re, Rue Montoyer, 12, B-1000 Bruxelles, Belgique
Institut de Statistique, Voie du Roman Pays, 20, B-1348 Louvain-la-Neuve, Belgique
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Abstract

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In this paper we will show how to set up a practical bonus-malus system with a finite number of classes. We will use the actual claim amount and claims frequency distributions in order to predict the future observed claims frequency when the new bonus-malus system will be in use. The future observed claims frequency is used to set up an optimal bonus-malus system as well as the transient and stationary distributions of the drivers in the new bonus-malus system. When the number of classes as well as the transition rules of the new bonus-malus system have been adopted, the premium levels are obtained by minimizing a certain distance between the levels of the practical bonus-malus system and the corresponding optimal bonus-malus system. Some iterations are necessary in order to reach stabilization of the future observed claims frequency and the levels of the practical bonus-malus system.

Keywords

Optimal bonus-malus systempractical bonus-malus systemhunger for bonusobserved claims frequency distributionactual claims frequency distributioniterative algorithmHofmann Distributionnon-parametric mixed Poisson fit
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 2 , November 2001 , pp. 317 - 335
Copyright
Copyright © International Actuarial Association 2001

References

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