IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i18p3906-d1239584.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/18/3906/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/18/3906/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, January.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Anja Breuer & Yves Staudt, 2022. "Equalization Reserves for Reinsurance and Non-Life Undertakings in Switzerland," Risks, MDPI, vol. 10(3), pages 1-41, March.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Denuit, Michel & Lang, Stefan, 2004. "Non-life rate-making with Bayesian GAMs," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 627-647, December.
    16. 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.
    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. Verschuren, Robert Matthijs, 2022. "Frequency-severity experience rating based on latent Markovian risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 379-392.
    2. 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.
    3. Tingting Chen & Anthony Francis Desmond & Peter Adamic, 2023. "Generalized Additive Modelling of Dependent Frequency and Severity Distributions for Aggregate Claims," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 12(4), pages 1-1.
    4. Freek Holvoet & Katrien Antonio & Roel Henckaerts, 2023. "Neural networks for insurance pricing with frequency and severity data: a benchmark study from data preprocessing to technical tariff," Papers 2310.12671, arXiv.org, revised Jan 2025.
    5. 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.
    6. Tzougas, George & Yik, Woo Hee & Mustaqeem, Muhammad Waqar, 2019. "Insurance ratemaking using the Exponential-Lognormal regression model," LSE Research Online Documents on Economics 101729, London School of Economics and Political Science, LSE Library.
    7. Ihsan Chaoubi & Camille Besse & H'el`ene Cossette & Marie-Pier C^ot'e, 2022. "Micro-level Reserving for General Insurance Claims using a Long Short-Term Memory Network," Papers 2201.13267, arXiv.org.
    8. Liivika Tee & Meelis Käärik & Rauno Viin, 2017. "On Comparison of Stochastic Reserving Methods with Bootstrapping," Risks, MDPI, vol. 5(1), pages 1-21, January.
    9. Yves L. Grize, 2015. "Applications of Statistics in the Field of General Insurance: An Overview," International Statistical Review, International Statistical Institute, vol. 83(1), pages 135-159, April.
    10. Deprez, Laurens & Antonio, Katrien & Boute, Robert, 2023. "Empirical risk assessment of maintenance costs under full-service contracts," European Journal of Operational Research, Elsevier, vol. 304(2), pages 476-493.
    11. Roel Verbelen & Katrien Antonio & Gerda Claeskens, 2018. "Unravelling the predictive power of telematics data in car insurance pricing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1275-1304, November.
    12. 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.
    13. Björkwall, Susanna & Hössjer, Ola & Ohlsson, Esbjörn & Verrall, Richard, 2011. "A generalized linear model with smoothing effects for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 27-37, July.
    14. 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.
    15. Emer Owens & Barry Sheehan & Martin Mullins & Martin Cunneen & Juliane Ressel & German Castignani, 2022. "Explainable Artificial Intelligence (XAI) in Insurance," Risks, MDPI, vol. 10(12), pages 1-50, December.
    16. Aivars Spilbergs & Andris Fomins & Māris Krastiņš, 2022. "Multivariate Modelling of Motor Third Party Liability Insurance Claims," European Journal of Business Science and Technology, Mendel University in Brno, Faculty of Business and Economics, vol. 8(1), pages 5-18.
    17. Emmanuel Jordy Menvouta & Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2022. "mCube: Multinomial Micro-level reserving Model," Papers 2212.00101, arXiv.org.
    18. Francis Duval & Mathieu Pigeon, 2019. "Individual Loss Reserving Using a Gradient Boosting-Based Approach," Risks, MDPI, vol. 7(3), pages 1-18, July.
    19. Thomas Poufinas & Periklis Gogas & Theophilos Papadimitriou & Emmanouil Zaganidis, 2023. "Machine Learning in Forecasting Motor Insurance Claims," Risks, MDPI, vol. 11(9), pages 1-19, September.
    20. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.

    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:gam:jmathe:v:11:y:2023:i:18:p:3906-:d:1239584. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.