Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T14:10:37.538Z Has data issue: false hasContentIssue false
  • English
  • Français

How to Define a Bonus-Malus System with an Exponential Utility Function*

Published online by Cambridge University Press:  29 August 2014

Jean Lemaire
Jean Lemaire*
Affiliation:
Université Libre de Bruxelles
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.

We compute a merit-rating system for automobile third party liability insurance by two different ways, both with the help of an exponential utility function.

(i) We apply the principle of zero utility to exponential utilities.

(ii) We break the symmetry between the overcharges and the undercharges by weighting them differently through the introduction of a utility function, in order to penalize the overcharges.

The results are applied to the portfolio of a Belgian company and compared to the premium system provided by the expected value principle.

Deux méthodes différentes, basées sur l'emploi de fonctions d'utilité exponentielles nous permettent de définir un système bonus-malus en assurance automobile:

(i) le principe de l'utilité nulle;

(ii) la pénalisation des injustices de la compagnie, obtenue en pondérant les erreurs de prime au moyen d'une fonction d'utilité de manière à briser la symétrie entre les primes trop élevées et les primes trop basses.

Les résultats théoriques sont appliqués au portefeuille d'une compagnie belge et comparés aux primes fournies par le principe de l'espérance mathématique.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 10 , Issue 3 , December 1979 , pp. 274 - 282
Copyright
Copyright © International Actuarial Association 1979

Footnotes

*

An earlier version of this paper was presented at the 14th ASTIN Colloquium, Taormina, October 1978.

References

REFERENCES

Bichsel, F. (1964). Erfahrungs-Tarifierung in der Motorfahrzeughaftpflicht-Versicherung; Mitteilungen der Vereinigung Schweizerischer Versicherungsmathernatiker, 64, 119–129.Google Scholar
Bühlmann, H. (1964). Optimale Prämienstufensysteme; Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 64, 193–213.Google Scholar
Corlier, F., Lemaire, J. and Muhokolo, D. (1979). Simulation of an automobile portfolio, The Geneva papers on risk and insurance, 12, 40–46.Google Scholar
Derron, M. (1962). Mathematische Probleme der Automobilversicherung; Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 62, 103–123.Google Scholar
Ferreira, J. (1977). Identifying Equitable Insurance Premiums for Risk Classes: An Alternative to the Classical Approach; presented at the XXIIIth International Meeting of the Institute of Management Sciences. Athens.Google Scholar
Gerber, H. (1974a). On additive premium calculation principles; ASTIN Bulletin, 7, 215–222.CrossRefGoogle Scholar
Gerber, H. (1974b). On iterative premium calculation principles; Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 74, 163–172.Google Scholar
Lemaire, J. (1977). Selection procedures of regression analysis applied to automobile insurance; Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 77, 65–72.Google Scholar