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Allowance for the Age of Claims in Bonus-Malus Systems*

  • Jean Pinquet (a1), Montserrat Guillén (a2) and Catalina Bolancé (a3)

Abstract

The purpose of the paper is to use the age of claims in the prediction of risks. A dynamic random effects model on longitudinal count data is presented, and estimated on the portfolio of a major Spanish insurance company. The estimated autocorrelation coefficients of stationary random effects are decreasing. A consequence is that the predictive ability of a claim decreases with the lag between the period of risk prediction and the period of occurrence. There is a wide gap between the long term properties of actuarial and real-world experience rating schemes. This gap can be partly filled if the age of claims is taken into account in the actuarial model.

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Copyright

Footnotes

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Pinquet acknowledges financial support from the Fédération Française des Sociétés d'Assurance. Guillén and Bolancé thank the Spanish CICYT grant SEC99-0693. We thank a referee for his comments.

Footnotes

References

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1.Besson, J.L. and Partrat, C. (1992) Trend et systèmes de bonus-malus. ASTIN Bulletin 22, 1132.
2.Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin 4, 199207.
3.Dionne, G. and Vanasse, C. (1989) A generalization of automobile insurance rating models: the negative binomial distribution with a regression component. ASTIN Bulletin 19, 199212.
4.Gerber, H. and Jones, D. (1975) Credibility formulas of the updating type. Transactions of the Society of Actuaries 27, 3152.
5.Henriet, D. and Rochet, J.C. (1986) La logique des systèmes bonus-malus en assurance automobile. Annales d'Economie et de Statistiques, 133152.
6.Lemaire, J. (1985) Automobile Insurance: Actuarial Models. Kluwer Academic Publishers.
7.Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers.
8.Pinquet, J., Guillen, M. and Bolance, C. (2000) Long-range contagion in automobile insurance data: Estimation and implications for experience rating. Working paper 2000-43, http://thema.u-parisl0.fr.
9.Sundt, B. (1988) Credibility estimators with geometric weights. Insurance: Mathematics and Economics 7, 113122.
10.Zeger, L.S. (1988) A regression model for time series of counts. Biometrika 74, 721729.

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