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Some Generalized Linear Models for the Estimation of the Mean Frequency of Claims in Motor Insurance

Author

Listed:
  • Mihaela COVRIG

    (The Bucharest University of Economic Studies)

  • Dumitru BADEA

    (The Bucharest University of Economic Studies)

Abstract

One of the most important problems that a non-life actuary faces is constructing a fair pricing. In particular, claim counts modeling is one of the components of motor insurance ratemaking. This paper aims to describe the econometric modeling of the mean frequency of claims in a motor insurance portfolio using generalized linear models. The main frequency distributions of count data are presented together with the generalized linear models. Numerical illustration presents and compares the different proposed regression models, using annual CASCO insurance data from a Romanian insurance company. The main findings are that the Negative Binomial regression model performs better than the Poisson model and quantifies overdispersion. The figures, the estimations and the tests are done in the open source soft R.

Suggested Citation

  • Mihaela COVRIG & Dumitru BADEA, 2017. "Some Generalized Linear Models for the Estimation of the Mean Frequency of Claims in Motor Insurance," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(4), pages 91-107.
    • Handle: RePEc:cys:ecocyb:v:50:y:2017:i:4:p:91-107
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    References listed on IDEAS

    as
    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    2. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2014. "Nonlife ratemaking and risk management with Bayesian generalized additive models for location, scale, and shape," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 225-249.
    3. Hilbe,Joseph M., 2014. "Modeling Count Data," Cambridge Books, Cambridge University Press, number 9781107611252, September.
    4. Boucher, Jean-Philippe & Inoussa, Rofick, 2014. "A Posteriori Ratemaking With Panel Data," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 587-612, September.
    5. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2014. "Nonlife ratemaking and risk management with Bayesian generalized additive models for location, scale, and shape," LIDAM Reprints ISBA 2014006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, September.
    7. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    8. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    claim counts modeling; count data; motor insurance; GLM; R.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C89 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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