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Modeling The Frequency Of Claims In Auto Insurance With Application To A French Case

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  • Mihaela DAVID

    () (Alexandru Ioan Cuza University of Iasi, Iasi, Roumania)

Abstract

The aim of this paper is to present the different models for count data used in the actuarial literature. In addition to the Poisson regression, Negative Binomial and Zero-Inflated models are applied to an auto insurance portfolio of a French insurance company. Statistical tests to evaluate the performance of the models are explained taking into consideration the difference between the nested and the non-nested models. The comparison between the nested models is performed using specification tests and the Vuong test is used to compare the fitting of non-nested models.

Suggested Citation

  • Mihaela DAVID, 2014. "Modeling The Frequency Of Claims In Auto Insurance With Application To A French Case," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 13, pages 69-85, June.
  • Handle: RePEc:aic:revebs:y:2014:i:13:davidm
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    References listed on IDEAS

    as
    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 19(02), pages 199-212, November.
    2. Dionne, G & Vanasse, C, 1992. "Automobile Insurance Ratemaking in the Presence of Asymmetrical Information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(2), pages 149-165, April-Jun.
    3. Denuit, Michel & Lang, Stefan, 2004. "Non-life rate-making with Bayesian GAMs," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 627-647, December.
    4. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    5. Cameron, A. Colin & Trivedi, Pravin K., 1990. "Regression-based tests for overdispersion in the Poisson model," Journal of Econometrics, Elsevier, vol. 46(3), pages 347-364, December.
    6. William H. Greene, 1994. "Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models," Working Papers 94-10, New York University, Leonard N. Stern School of Business, Department of Economics.
    7. Jean‐Philippe Boucher & Michel Denuit & Montserrat Guillen, 2009. "Number of Accidents or Number of Claims? An Approach with Zero‐Inflated Poisson Models for Panel Data," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 821-846, December.
    8. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    9. Antonio, Katrien & Frees, Edward W. & Valdez, Emiliano A., 2010. "A Multilevel Analysis of Intercompany Claim Counts," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 40(01), pages 151-177, May.
    10. Gourieroux, C. & Jasiak, J., 2004. "Heterogeneous INAR(1) model with application to car insurance," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 177-192, April.
    11. 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.
    12. Gurmu, Shiferaw, 1991. "Tests for Detecting Overdispersion in the Positive Poisson Regression Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 215-222, April.
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    More about this item

    Keywords

    Frequency of claims; count data models; over dispersion; zero inflation; models comparison; specification tests; Vuong test;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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