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Tariff Analysis in Automobile Insurance: Is It Time to Switch from Generalized Linear Models to Generalized Additive Models?

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  • Zuleyka Díaz Martínez

    (Group of Analysis, Security and Systems (GASS), Department of Financial and Actuarial Economics & Statistics, Faculty of Economics and Business Administration, Universidad Complutense de Madrid (UCM), Campus Somosaguas, 28223 Madrid, Spain
    These authors contributed equally to this work.)

  • José Fernández Menéndez

    (Department of Business Administration, Faculty of Economics and Business Administration, Universidad Complutense de Madrid (UCM), Campus Somosaguas, 28223 Madrid, Spain
    These authors contributed equally to this work.)

  • Luis Javier García Villalba

    (Group of Analysis, Security and Systems (GASS), Department of Software Engineering and Artificial Intelligence (DISIA), Faculty of Computer Science and Engineering, Office 431, Universidad Complutense de Madrid (UCM), Calle Profesor José García Santesmases, 9, Ciudad Universitaria, 28040 Madrid, Spain
    These authors contributed equally to this work.)

Abstract

Generalized Linear Models (GLMs) are the standard tool used for pricing in the field of automobile insurance. Generalized Additive Models (GAMs) are more complex and computationally intensive but allow taking into account nonlinear effects without the need to discretize the explanatory variables. In addition, they fit perfectly into the mental framework shared by actuaries and are easier to use and interpret than machine learning models, such as trees or neural networks. This work compares both the GLM and GAM approaches, using a wide sample of policies to assess their differences in terms of quality of predictions, complexity of use, and time of execution. The results show that GAMs are a powerful alternative to GLMs, particularly when “big data” implementations of GAMs are used.

Suggested Citation

  • Zuleyka Díaz Martínez & José Fernández Menéndez & Luis Javier García Villalba, 2023. "Tariff Analysis in Automobile Insurance: Is It Time to Switch from Generalized Linear Models to Generalized Additive Models?," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3906-:d:1239584
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    References listed on IDEAS

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    1. Denuit, Michel & Hainaut, Donatien & Trufin, Julien, 2020. "Effective Statistical Learning Methods for Actuaries II : Tree-Based Methods and Extensions," LIDAM Reprints ISBA 2020035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Yves Staudt & Joël Wagner, 2021. "Assessing the Performance of Random Forests for Modeling Claim Severity in Collision Car Insurance," Risks, MDPI, vol. 9(3), pages 1-28, March.
    3. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    4. Katrien Antonio & Jan Beirlant, 2008. "Issues in Claims Reserving and Credibility: A Semiparametric Approach With Mixed Models," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 643-676, September.
    5. Łukasz Delong & Mario V. Wüthrich, 2020. "Neural Networks for the Joint Development of Individual Payments and Claim Incurred," Risks, MDPI, vol. 8(2), pages 1-34, April.
    6. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    7. Jean-Thomas Baillargeon & Luc Lamontagne & Etienne Marceau, 2020. "Mining Actuarial Risk Predictors in Accident Descriptions Using Recurrent Neural Networks," Risks, MDPI, vol. 9(1), pages 1-14, December.
    8. Roel Henckaerts & Marie-Pier Côté & Katrien Antonio & Roel Verbelen, 2021. "Boosting Insights in Insurance Tariff Plans with Tree-Based Machine Learning Methods," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(2), pages 255-285, April.
    9. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    10. Hossein Hassani & Emmanuel Sirimal Silva, 2015. "A Kolmogorov-Smirnov Based Test for Comparing the Predictive Accuracy of Two Sets of Forecasts," Econometrics, MDPI, vol. 3(3), pages 1-20, August.
    11. Denuit, Michel & Lang, Stefan, 2004. "Non-life rate-making with Bayesian GAMs," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 627-647, December.
    12. Mahmoudvand, Rahim & Hassani, Hossein, 2009. "Generalized Bonus-Malus Systems with a Frequency and a Severity Component on an Individual Basis in Automobile Insurance," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 307-315, May.
    13. Yuxuan Tan & Zurui Zeng & Huanzhu Liang & Xueqiong Weng & Huojie Yao & Yingyin Fu & Yexin Li & Jingmin Chen & Xiangcai Wei & Chunxia Jing, 2022. "Association between Perfluoroalkyl and Polyfluoroalkyl Substances and Women’s Infertility, NHANES 2013–2016," IJERPH, MDPI, vol. 19(22), pages 1-15, November.
    14. Jessica Pesantez-Narvaez & Montserrat Guillen & Manuela Alcañiz, 2019. "Predicting Motor Insurance Claims Using Telematics Data—XGBoost versus Logistic Regression," Risks, MDPI, vol. 7(2), pages 1-16, June.
    15. Verschuren, Robert Matthijs, 2021. "Predictive Claim Scores For Dynamic Multi-Product Risk Classification In Insurance," ASTIN Bulletin, Cambridge University Press, vol. 51(1), pages 1-25, January.
    16. Anja Breuer & Yves Staudt, 2022. "Equalization Reserves for Reinsurance and Non-Life Undertakings in Switzerland," Risks, MDPI, vol. 10(3), pages 1-41, March.
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