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On the Use of Conditional Specification Models in Claim Count Distributions: an Application to Bonus-Malus Systems

Published online by Cambridge University Press:  17 April 2015

José María Sarabia ,
Emilio Gómez-Déniz  and
Francisco J. Vázquez-Polo
José María Sarabia
Affiliation:
Department of Quantitative Methods, University of Las Palmas de Gran Canaria, 35017-Las Palmas de Gran Canaria, Spain, E-mail: fjvpolo@dmc.ulpgc.es
Emilio Gómez-Déniz
Affiliation:
Department of Economics, University of Cantabria, 39005-Santander, Spain, E-mail: sarabiaj@unican.es
Francisco J. Vázquez-Polo
Affiliation:
Department of Quantitative Methods, University of Las Palmas de Gran Canaria, 35017-Las Palmas de Gran Canaria, Spain, E-mail: egomez@dmc.ulpgc.es
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Abstract

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In this paper a new methodology using the conditional specification technique intoduced by Arnold et al. (1999) is used to obtain bonus-malus premiums. A Poisson distribution for which the parameter is a function of the classical structure parameter is used and a new class of prior distribution arises in a natural way. This model contains, as a particular case, the classical compound Poisson model and is found to be much more robust than earlier ones. An example is given to illustrate our ideas.

Keywords

Conditional Specification ModelGeneralized Negative Binomial DistributionBonus-Malus systems
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 34 , Issue 1 , May 2004 , pp. 85 - 98
Copyright
Copyright © ASTIN Bulletin 2004

Footnotes

1

Department of Economics, University of Cantabria, 39005-Santander, Spain. E-mail: sarabiaj@unican.es

2

Department of Quantitative Methods in Economics, University of Las Palmas de Gran Canaria, 35017-Las Palmas de G.C., Spain. E-mail: {egomez or fjvpolo}@dmc.ulpgc.es

References

Arnold, B.C, Castillo, E. and Sarabia, J.M. (1999). Conditional Specification of Statistical Models. Springer Series in Statistics, Springer Verlag, New York.Google Scholar
Arnold, B.C., Castillo, E. and Sarabia, J.M. (2001) Conditionally Specified Distributions: An Introduction (with discussion). Statistical Science, 16(3), 249–274.CrossRefGoogle Scholar
Consul, P.C. and Jain, G.C. (1973) A generalization of the Poisson distribution. Technometrics, 15(4), 791–799.CrossRefGoogle Scholar
Davis, P. and Rabinowitz, P. (1984) Methods of numerical integration. San Diego: Academic Press.Google 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
Gerber, H. (1991) From the generalized gamma to the generalized negative binomial distribution. Insurance: Mathematics & Economics, 10, 303–309.Google Scholar
Gómez, E., Pérez, J., Hernández, A. and Vázquez-Polo, F.J. (2002) Measuring sensitivity in a Bonus-Malus System. Insurance: Mathematics & Economics, 31, 105–113.Google Scholar
Goovaerts, M.J. and Kaas, R. (1991) Evaluating compound generalized Poisson distributions recursively. ASTIN Bulletin, 21, 193–197.CrossRefGoogle Scholar
Lemaire, J. (1979) How to define a Bonus-Malus system with an exponential utility function. Astin Bulletin, 10, 274–282.CrossRefGoogle Scholar
Lemaire, J. (1985) Automobile Insurance (Actuarial Models). Kluwer-Nijhoff Publishing. Boston/Dordrecht/Lancaster.CrossRefGoogle Scholar
Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers. Boston/Dordrecht/Londres.CrossRefGoogle Scholar
Lemaire, J. and Zi, H. (1994) High deductibles instead of Bonus-Malus: can it work? Astin Bulletin, 24(1), 75–88.CrossRefGoogle Scholar
Leroux, B.G. (1992) Consistent estimation of a mixing distribution. Annals of Statistics, 20(3), 1350–1360.CrossRefGoogle Scholar
Panjer, H.H. and Willmot, G.E. (1988) Motivating claims frequency models, in Proceedings of the twenty-third international congress of actuaries, Helsinki, 3, 269–284.Google Scholar
Scollnik, D.P.M. (1995) The Bayesian analysis of generalized Poisson models for claim frequency data utilising Markov chain Monte Carlo, in Proceedings of the 29th Actuarial Research Conference, Actuarial Research Clearing House.Google Scholar
Sichel, H. (1971) On a family of discrete distribution particularly suited to represent long-tailed frequency data, in Proceedings of the Third Symposium on Mathematical Statistics, ed. Laubscher, N.F., Pretoria.Google Scholar
Willmot, G.E. (1987) The Poisson-Inverse Gaussian distribution as an alternative to the negative binomial. Scandinavian Actuarial Journal, 113–127.CrossRefGoogle Scholar