IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

A priori ratemaking using bivariate poisson regression models

  • Lluis Bermúdez i Morata

    ()

    (RFA-IREA, Universitat de Barcelona.)

Registered author(s):

    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.

    If 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.

    File URL: http://www.pcb.ub.es/xreap/aplicacio/fitxers/XREAP2008-09.pdf
    File Function: First version, 2008
    Download Restriction: no

    File URL: http://www.pcb.ub.es/xreap/aplicacio/fitxers/XREAP2008-09.pdf
    File Function: Revised version, 2008
    Download Restriction: no

    Paper provided by Xarxa de Referència en Economia Aplicada (XREAP) in its series Working Papers with number XREAP2008-09.

    as
    in new window

    Length: 27 pages
    Date of creation: Jul 2008
    Date of revision: Jul 2008
    Handle: RePEc:xrp:wpaper:xreap2008-09
    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
    Phone: +34+934039653
    Web page: http://www.pcb.ub.edu/xreap
    Email:


    More information through EDIRC

    References listed on IDEAS
    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.:

    as in new window
    1. 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.
    2. Partrat, Christian, 1994. "Compound model for two dependent kinds of claim," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 219-231, December.
    3. 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.
    4. 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.
    5. de Lourdes Centeno, Maria, 2005. "Dependent risks and excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 229-238, October.
    6. J. F. Walhin, 2003. "Bivariate Hofmann distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(9), pages 1033-1046.
    7. 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.
    8. 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.
    9. J. Pinquet, 1997. "Experience rating through heterogeneous models," THEMA Working Papers 97-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    10. 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.
    11. 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.
    12. 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).
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    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.

    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 you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.