IDEAS home Printed from https://ideas.repec.org/a/aic/revebs/y2014i13davidm.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://rebs.feaa.uaic.ro/articles/pdfs/169.pdf
    Download Restriction: no
    ---><---

    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, Cambridge University Press, vol. 19(2), 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. Katrien Antonio & Emiliano Valdez, 2012. "Statistical concepts of a priori and a posteriori risk classification in insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 187-224, June.
    5. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Antonio, Katrien & Frees, Edward W. & Valdez, Emiliano A., 2010. "A Multilevel Analysis of Intercompany Claim Counts," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 151-177, May.
    11. 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.
    12. 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.
    13. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Mihaela & Jemna Dănuţ-Vasile, 2015. "Modeling the Frequency of Auto Insurance Claims by Means of Poisson and Negative Binomial Models," Scientific Annals of Economics and Business, Sciendo, vol. 62(2), pages 151-168, July.
    2. Payandeh Najafabadi Amir T. & MohammadPour Saeed, 2018. "A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate–Making Systems," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(2), pages 1-31, July.
    3. Dahen, Hela & Dionne, Georges, 2010. "Scaling models for the severity and frequency of external operational loss data," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1484-1496, July.
    4. 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.
    5. Christopher J. W. Zorn, 1998. "An Analytic and Empirical Examination of Zero-Inflated and Hurdle Poisson Specifications," Sociological Methods & Research, , vol. 26(3), pages 368-400, February.
    6. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    7. Tzougas, George & Hoon, W. L. & Lim, J. M., 2019. "The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking," LSE Research Online Documents on Economics 101728, London School of Economics and Political Science, LSE Library.
    8. Kornelius Kraft & Jörg Stank & Ralf Dewenter, 2011. "Co-determination and innovation," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 35(1), pages 145-172.
    9. Denise Desjardins & Georges Dionne & Yang Lu, 2023. "Hierarchical random‐effects model for the insurance pricing of vehicles belonging to a fleet," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(2), pages 242-259, March.
    10. George Tzougas, 2020. "EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking," Risks, MDPI, vol. 8(3), pages 1-23, September.
    11. Katrien Antonio & Emiliano Valdez, 2012. "Statistical concepts of a priori and a posteriori risk classification in insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 187-224, June.
    12. Tzougas, George, 2020. "EM estimation for the Poisson-Inverse Gamma regression model with varying dispersion: an application to insurance ratemaking," LSE Research Online Documents on Economics 106539, London School of Economics and Political Science, LSE Library.
    13. William Greene, 2009. "Models for count data with endogenous participation," Empirical Economics, Springer, vol. 36(1), pages 133-173, February.
    14. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2006. "Vehicle and Fleet Random Effects in a Model of Insurance Rating for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 25-77, May.
    15. Greene, William, 2007. "Functional Form and Heterogeneity in Models for Count Data," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(2), pages 113-218, August.
    16. Niklas Elert, 2014. "What determines entry? Evidence from Sweden," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(1), pages 55-92, August.
    17. Gning, Lucien & Diagne, M.L. & Tchuenche, J.M., 2023. "Hierarchical generalized linear models, correlation and a posteriori ratemaking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    18. Ulf‐ G. Gerdtham, 1997. "Equity in Health Care Utilization: Further Tests Based on Hurdle Models and Swedish Micro Data," Health Economics, John Wiley & Sons, Ltd., vol. 6(3), pages 303-319, May.
    19. Hugo Pinto & Manuel Fernández-Esquinas, 2013. "Exploring knowledge-transfer dynamics in a South European region: breadth, intensity and informality of university-industry interactions in Andalusia," Chapters, in: Tüzin Baycan (ed.), Knowledge Commercialization and Valorization in Regional Economic Development, chapter 10, pages 209-237, Edward Elgar Publishing.
    20. Drivas, Kyriakos & Economidou, Claire & Karamanis, Dimitrios & Sanders, Mark, 2020. "Mobility of highly skilled individuals and local innovation activity," Technological Forecasting and Social Change, Elsevier, vol. 158(C).

    More about this item

    Keywords

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

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aic:revebs:y:2014:i:13:davidm. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sireteanu Napoleon-Alexandru (email available below). General contact details of provider: https://edirc.repec.org/data/feaicro.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.