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

Jean Lemaire

ASTIN Bulletin, 1979, vol. 10, issue 3, 274-282

Abstract: 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.

Date: 1979
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