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Using Mixed Poisson Processes in Connection with Bonus-Malus Systems1

Published online by Cambridge University Press:  29 August 2014

J.F. Walhin  and
J. Paris
J.F. Walhin*
Affiliation:
Institut de Statistique, Université Catholique de Louvain, Belgium Le Mans Assurances, Belgique
J. Paris*
Affiliation:
Institut de Statistique, Université Catholique de Louvain, Belgium
*
Institut de Statistique, Voie du Roman Pays, 20, B-1348 Louvain-la-Neuve, Belgium
Institut de Statistique, Voie du Roman Pays, 20, B-1348 Louvain-La-Neuve, Belgium
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Abstract

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For the construction of bonus-malus systems, we propose to show how to apply, thanks to simple mathematics, a parametric method encompassing those encountered in the literature. We also compare this parametric method with a non-parametric one that has not yet been used in the actuarial literature and that however permits a simple formulation of the stationary and transition probabilities in a portfolio whenever we have the intention to construct a bonus-malus system with finite number of classes.

Keywords

Mixed Poisson processesnon-parametric estimationHofmann's distributionBayes theorembonus-malus systemsstationary distribution
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 1 , May 1999 , pp. 81 - 99
Copyright
Copyright © International Actuarial Association 1999

Footnotes

1

This paper has been presented at the XXVIIIth ASTIN Colloquium, Cairns 10-13 August 1997

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