Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-29T00:57:07.331Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Coene, G. and Doray, L.G. (1996). A Financially Balanced Bonus-Malus System. Astin Bulletin, 26:101–115.CrossRefGoogle Scholar
Lemaire, J. (1977). La Soif du Bonus. Astin Bulletin, 9: 181–190.CrossRefGoogle Scholar
Lemaire, J. (1995). Bonus-Malus Systems in Automobile Insurance. Boston: Kluwer.CrossRefGoogle Scholar
Simar, L. (1976). Maximum Likelihood Estimation of a Compound Poisson Process. The Annals of Statistics, 4: 1200–1209.CrossRefGoogle Scholar
Walhin, J.F. and Paris, J. (1999a). Processus de Poisson Mélange et Formules Unifiées pour Systèmes Bonus-Malus. Bulletin Français d'Actuariat, 3: 35–43.Google Scholar
Walhin, J.F. and Paris, J. (1999b). Using Mixed Poisson Distributions in Connection with Bonus-Malus systems. Astin Bulletin, 29: 81–99.CrossRefGoogle Scholar
Walhin, J.F. and Paris, J. (2001). The Actual Claim Amount and Frequency Distributions within a Bonus-Malus System. To be published in Astin Bulletin.Google Scholar