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Design of Optimal Bonus-Malus Systems With a Frequency and a Severity Component On an Individual Basis in Automobile Insurance

Published online by Cambridge University Press:  29 August 2014

Nicholas E. Frangos  and
Spyridon D. Vrontos
Nicholas E. Frangos
Affiliation:
Department of Statistics, Athens University of Economics and Business, Patission 76, 10434, Athens, Greece, E-mail:nef@aueb.gr and svrontos@aueb.gr
Spyridon D. Vrontos
Affiliation:
Department of Statistics, Athens University of Economics and Business, Patission 76, 10434, Athens, Greece, E-mail:nef@aueb.gr and svrontos@aueb.gr
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Abstract

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The majority of optimal Bonus-Malus Systems (BMS) presented up to now in the actuarial literature assign to each policyholder a premium based on the number of his accidents. In this way a policyholder who had an accident with a small size of loss is penalized unfairly in the same way with a policyholder who had an accident with a big size of loss. Motivated by this, we develop in this paper, the design of optimal BMS with both a frequency and a severity component. The optimal BMS designed are based both on the number of accidents of each policyholder and on the size of loss (severity) for each accident incurred. Optimality is obtained by minimizing the insurer's risk. Furthermore we incorporate in the above design of optimal BMS the important a priori information we have for each policyholder. Thus we propose a generalised BMS that takes into consideration simultaneously the individual's characteristics, the number of his accidents and the exact level of severity for each accident.

Keywords

Optimal BMSclaim frequencyclaim severityquadratic loss functiona priori classification criteriaa posteriori classification criteria
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 1 , May 2001 , pp. 1 - 22
Copyright
Copyright © International Actuarial Association 2001

References

Baxter, L.A., Coutts, S.M. and Ross, G.A.F. (1979) Applications of Linear Models in Motor Insurance. 21st International Congress of Actuaries.Google Scholar
Bichsel, F. (1964) Erfahrung-Tarifieung in der Motorfahrzeug-haftplichtversiherung, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 119–129.Google Scholar
Buhlmann, H. (1964) Optimale Pramienstufensysteme, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker 193–213.Google Scholar
Coene, G. and Doray, L.G. (1996) A Financially Balanced Bonus-Malus System. Astin Bulletin 26, 107–115.CrossRefGoogle Scholar
Dionne, G. and Vanasse, C. (1989) A generalization of actuarial automobile insurance rating models: the negative binomial distribution with a regression component, Astin Bulletin 19, 199–212.CrossRefGoogle Scholar
Dionne, G. and Vanasse, C. (1992) Automobile insurance ratemaking in the presence of asymmetrical information, Journal of Applied Econometrics 7, 149–165.CrossRefGoogle Scholar
Ferreira, J. (1974) The long term effect of merit-rating plans on individual motorists, Operations Research, 22, 954–978.CrossRefGoogle Scholar
Gourieroux, C., Montfort, A. and Trognon, A. (1984a) Pseudo maximum likelihood methods: theory, Econometrica, 52, 681–700.CrossRefGoogle Scholar
Gourieroux, C., Montfort, A. and Trognon, A. (1984b) Pseudo maximum likelihood methods: application to Poisson models, Econometrica, 52, 701–720.CrossRefGoogle Scholar
Hausmann, J.A., Hall, B.H. and Griliches, Z. (1984) Econometric models for count data with an application to the patents-R&D relationship, Econometrica, 46, 1251–1271.Google Scholar
Herzog, T. (1996) Introduction to Credibility Theory. Actex Publications, Winstead.Google Scholar
Hogg, R.V. and Klugman, S.A. (1984) Loss Distributions, John Wiley & Sons, New York.CrossRefGoogle Scholar
McCullagh, P. and Nelder, J.A. (1983, 1989) Generalized Linear Models. Chapman & Hall.CrossRefGoogle Scholar
Lawless, J.F. (1987) Negative Binomial Distribution and Mixed Poisson Regression, Canadian Journal of Statistics, 15, 3, 209–225.CrossRefGoogle Scholar
Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance, Kluwer Academic Publishers, Massachusetts.CrossRefGoogle Scholar
Picard, P. (1976) Generalisation de l'etude sur la survenance des sinistres en assurance automobile, Bulletin Trimestriel de l'Institute des Actuaires Francais, 204–267.Google Scholar
Picech, L. (1994) The Merit-Rating Factor in a Multiplicating Rate-Making model. Astin Colloquium, Cannes.Google Scholar
Pinquet, (1997) Allowance for Costs of Claims in Bonus-Malus Systems, Astin Bulletin, 27, 33–57.CrossRefGoogle Scholar
Pinquet, J. (1998) Designing Optimal Bonus-Malus Systems From Different Types of Claims. Astin Bulletin, 28, 205–220.CrossRefGoogle Scholar
Renshaw, A.E. (1994) Modelling The Claims Process in the Presence of Covariates. Astin Bulletin, 24, 265–285.CrossRefGoogle Scholar
Sigalotti, (1994) Equilibrium Premiums in a Bonus-Malus System, Astin Colloquium, Cannes.Google Scholar
Taylor, G. (1997) Setting A Bonus-Malus Scale in the Presence of Other Rating Factors. Astin Bulletin, 27, 319–327.CrossRefGoogle Scholar
Tremblay, L. (1992) Using the Poisson Inverse Gaussian in Bonus-Malus Systems, Astin Bulletin 22, 97–106.CrossRefGoogle Scholar
Vrontos, S. (1998) Design of an Optimal Bonus-Malus System in Automobile Insurance. Msc. Thesis, Department of Statistics, Athens University of Economics and Business, ISBN: 960-7929-21-7.Google Scholar
Walhin, J.F. and Paris, J. (1999) Using Mixed Poisson distributions in connection with Bonus-Malus Systems. Astin Bulletin 29, 81–99.CrossRefGoogle Scholar