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

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  • Lemaire, Jean

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.

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  • Lemaire, Jean, 1979. "How to Define a Bonus-Malus System with an Exponential Utility Function," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 274-282, December.
    • Handle: RePEc:cup:astinb:v:10:y:1979:i:03:p:274-282_00
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    1. Gomez, E. & Hernandez, A. & Perez, J. M. & Vazquez-Polo, F. J., 2002. "Measuring sensitivity in a bonus-malus system," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 105-113, August.
    2. Agata Boratyńska, 2021. "Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 123-140, September.
    3. Boratyńska Agata, 2021. "Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss," Statistics in Transition New Series, Statistics Poland, vol. 22(3), pages 123-140, September.
    4. Ojeda, Enrique Calderín & Déniz, Emilio Gómez & Cabrera Ortega, Ignacio J., 2007. "Bayesian local robustness under weighted squared-error loss function incorporating unimodality," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 69-74, January.
    5. V'ictor Blanco & Jos'e M. P'erez-S'anchez, 2015. "On the aggregation of experts' information in Bonus-Malus systems," Papers 1511.03876, arXiv.org, revised Nov 2016.
    6. Morillo, Isabel & Bermudez, Lluis, 2003. "Bonus-malus system using an exponential loss function with an Inverse Gaussian distribution," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 49-57, August.
    7. Emilio Gomez-deniz & Francisco Vazquez-polo, 2005. "Modelling uncertainty in insurance Bonus-Malus premium principles by using a Bayesian robustness approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 771-784.
    8. Gómez-Déniz, Emilio & Sarabia, José Mari­a & Calderi­n-Ojeda, Enrique, 2008. "Univariate and multivariate versions of the negative binomial-inverse Gaussian distributions with applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 39-49, February.
    9. Agustin Hernandez Bastida & Emilio Gomez Deniz & Jose Maria Perez Sanchez, 2009. "Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(8), pages 853-869.
    10. Villar Frexedas, Oscar & Vayá, Esther, 2005. "Financial Contagion between Economies: an Exploratory Spatial Analysis/Contagio financiero entre economías: Un análisis exploratorio espacial," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 23, pages 151-165, Abril.
    11. Serpil Bülbül & Kemal Baykal, 2016. "Optimal Bonus-Malus System Design in Motor Third-Party Liability Insurance in Turkey: Negative Binomial Model," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 8(8), pages 205-205, August.

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