A priori ratemaking using bivariate poisson regression models
In automobile insurance, it is useful to achieve a priori ratemaking by resorting to generalized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper examines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tariff system might be affected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.
|Date of creation:||Jul 2008|
|Date of revision:||Jul 2008|
|Contact details of provider:|| Postal: |
Web page: http://www.pcb.ub.edu/xreap
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Partrat, Christian, 1994. "Compound model for two dependent kinds of claim," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 219-231, December.
- J. Pinquet, 1997. "Experience rating through heterogeneous models," THEMA Working Papers 97-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
- Dimitris Karlis & Ioannis Ntzoufras, . "Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R," Journal of Statistical Software, American Statistical Association, vol. 14(i10).
- Dionne, G. & Vanasse, C., 1988.
"A Generalization Of Automobile Insurance Rating Models: The Negative Binomial Distribution With A Regression Component,"
Cahiers de recherche
8833, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Dionne, G. & Vanasse, C., 1988. "A Generalization of Automobile Insurance Rating Models: the Negative Binomial Distribution with a Regression Component," Cahiers de recherche 8833, Universite de Montreal, Departement de sciences economiques.
- C. Bolancé & M. Guillén & J. Pinquet, 2002.
"Time-varying credibility for frequency risk models : Estimation and tests for autoregressive specifications on the random effects,"
THEMA Working Papers
2002-18, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Bolance, Catalina & Guillen, Montserrat & Pinquet, Jean, 2003. "Time-varying credibility for frequency risk models: estimation and tests for autoregressive specifications on the random effects," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 273-282, October.
- J. F. Walhin, 2003. "Bivariate Hofmann distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(9), pages 1033-1046.
- Ambagaspitiya, Rohana S., 1999. "On the distributions of two classes of correlated aggregate claims," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 301-308, May.
- de Lourdes Centeno, Maria, 2005. "Dependent risks and excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 229-238, October.
- J. Pinquet & M. Guillén & C. Bolancé, 2000. "Long-range contagion in automobile insurance data : estimation and implications for experience rating," THEMA Working Papers 2000-43, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Boucher, Jean-Philippe & Denuit, Michel, 2008. "Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 727-735, April.
- Jung, Robert C & Winkelmann, Rainer, 1993. "Two Aspects of Labor Mobility: A Bivariate Poisson Regression Approach," Empirical Economics, Springer, vol. 18(3), pages 543-56.
When requesting a correction, please mention this item's handle: RePEc:xrp:wpaper:xreap2008-09. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.