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Generalized linear models for dependent frequency and severity of insurance claims

Author

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  • Garrido, J.
  • Genest, C.
  • Schulz, J.

Abstract

Traditionally, claim counts and amounts are assumed to be independent in non-life insurance. This paper explores how this often unwarranted assumption can be relaxed in a simple way while incorporating rating factors into the model. The approach consists of fitting generalized linear models to the marginal frequency and the conditional severity components of the total claim cost; dependence between them is induced by treating the number of claims as a covariate in the model for the average claim size. In addition to being easy to implement, this modeling strategy has the advantage that when Poisson counts are assumed together with a log-link for the conditional severity model, the resulting pure premium is the product of a marginal mean frequency, a modified marginal mean severity, and an easily interpreted correction term that reflects the dependence. The approach is illustrated through simulations and applied to a Canadian automobile insurance dataset.

Suggested Citation

  • Garrido, J. & Genest, C. & Schulz, J., 2016. "Generalized linear models for dependent frequency and severity of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 205-215.
  • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:205-215
    DOI: 10.1016/j.insmatheco.2016.06.006
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    References listed on IDEAS

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    Cited by:

    1. Park, Sojung C. & Kim, Joseph H.T. & Ahn, Jae Youn, 2018. "Does hunger for bonuses drive the dependence between claim frequency and severity?," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 32-46.
    2. Yang Lu, 2019. "Flexible (panel) regression models for bivariate count–continuous data with an insurance application," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1503-1521, October.
    3. Tatjana Miljkovic & Daniel Fernández, 2018. "On Two Mixture-Based Clustering Approaches Used in Modeling an Insurance Portfolio," Risks, MDPI, Open Access Journal, vol. 6(2), pages 1-18, May.
    4. Jeong, Himchan & Valdez, Emiliano A., 2020. "Predictive compound risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 182-195.
    5. Roland R. Ramsahai, 2020. "Connecting actuarial judgment to probabilistic learning techniques with graph theory," Papers 2007.15475, arXiv.org.
    6. Denuit, Michel & Lu, Yang, 2020. "Wishart-Gamma mixtures for multiperil experience ratemaking, frequency-severity experience rating and micro-loss reserving," LIDAM Discussion Papers ISBA 2020016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Cossette, Hélène & Marceau, Etienne & Mtalai, Itre, 2019. "Collective risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 153-168.
    8. Mary Kelly & Zilin Wang, 2020. "A data set for modeling claims processes—TSA claims data," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 23(3), pages 269-276, September.
    9. Laudagé, Christian & Desmettre, Sascha & Wenzel, Jörg, 2019. "Severity modeling of extreme insurance claims for tariffication," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 77-92.
    10. Shengkun Xie & Anna T. Lawniczak, 2018. "Estimating Major Risk Factor Relativities in Rate Filings Using Generalized Linear Models," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(4), pages 1-14, October.
    11. Pierre-Olivier Goffard & Patrick Laub, 2020. "Approximate Bayesian Computations to fit and compare insurance loss models," Working Papers hal-02891046, HAL.
    12. Mengyu Yu & Mazie Krehbiel & Samantha Thompson & Tatjana Miljkovic, 2020. "An exploration of gender gap using advanced data science tools: actuarial research community," Scientometrics, Springer;Akadémiai Kiadó, vol. 123(2), pages 767-789, May.
    13. Wenhui Zhang & Yongmin Su & Ruimin Ke & Xinqiang Chen, 2018. "Evaluating the influential priority of the factors on insurance loss of public transit," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-11, January.
    14. Gian Paolo Clemente & Pierpaolo Marano, 2020. "The broker model for peer-to-peer insurance: an analysis of its value," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 45(3), pages 457-481, July.
    15. Baak, M. & Koopman, R. & Snoek, H. & Klous, S., 2020. "A new correlation coefficient between categorical, ordinal and interval variables with Pearson characteristics," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    16. Oh, Rosy & Lee, Youngju & Zhu, Dan & Ahn, Jae Youn, 2021. "Predictive risk analysis using a collective risk model: Choosing between past frequency and aggregate severity information," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 127-139.
    17. Lee, Gee Y. & Shi, Peng, 2019. "A dependent frequency–severity approach to modeling longitudinal insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 115-129.
    18. Xiaoshan Su & Manying Bai, 2020. "Stochastic gradient boosting frequency-severity model of insurance claims," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-24, August.

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