A priori ratemaking using bivariate poisson regression models
AbstractIn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Xarxa de Referència en Economia Aplicada (XREAP) in its series Working Papers with number XREAP2008-09.
Length: 27 pages
Date of creation: Jul 2008
Date of revision: Jul 2008
Contact details of provider:
Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques i Empresarials, Universitat de Barcelona, c/ Tinent Coronel Valenzuela, 1-11, 08034 Barcelona
Web page: http://www.pcb.ub.edu/xreap
More information through EDIRC
This paper has been announced in the following NEP Reports:
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.:
- 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.
- 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.
- 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.
- J. Pinquet, 1997. "Experience rating through heterogeneous models," THEMA Working Papers 97-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- 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.
- 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.
- 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.
- Partrat, Christian, 1994. "Compound model for two dependent kinds of claim," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 219-231, December.
- 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. F. Walhin, 2003. "Bivariate Hofmann distributions," Journal of Applied Statistics, Taylor and Francis Journals, vol. 30(9), pages 1033-1046.
- 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.
- 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.
- 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).
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: () The email address of this maintainer does not seem to be valid anymore. Please ask to update the entry or send us the correct address.
If references are entirely missing, you can add them using this form.