IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p334-d1029312.html
   My bibliography  Save this article

Generalised Additive Modelling of Auto Insurance Data with Territory Design: A Rate Regulation Perspective

Author

Listed:
  • Shengkun Xie

    (Global Management Studies, Ted Rogers School of Management, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada)

  • Kun Shi

    (Global Management Studies, Ted Rogers School of Management, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada)

Abstract

Pricing using a Generalised Linear Model is the gold standard in the auto insurance industry and rate regulation. Generalised Additive Model applications in insurance pricing are receiving increasing attention from academic researchers and actuarial pricing professionals. The actuarial practice has constantly shown evidence of significantly different premium rates among the different rating territories. In this work, we build predictive models for claim frequency and severity using the synthetic Usage Based Insurance (UBI) dataset variables. First, we conduct territorial clustering based on each location’s claim counts and amounts by grouping those locations into a smaller set, defined as a cluster for rating purposes. After clustering, we incorporate these clusters into our predictive model to determine the risk relativity for each factor level. Through predictive modelling, we have successfully identified key factors that may be helpful for the rate regulation of UBI. Our work aims to fill the gap between individual-level pricing and rate regulation using the UBI database and provides insights on consistency in using traditional rating variables for UBI pricing. Our main contribution is to outline how GAM can address a more complicated functionality of risk factors and the interactions among them. We also contribute to demonstrating the territory clustering problem in UBI to construct the rating territories for pricing and rate regulation. We find that relativity for high annual mileage driven is almost three times that associated with low annual mileage level, which implies its importance in premium calculation. Overall, we provide insights into how UBI can be regulated through traditional pricing factors, additional factors from UBI datasets and rating territories derived from basic rating units and the driver’s location.

Suggested Citation

  • Shengkun Xie & Kun Shi, 2023. "Generalised Additive Modelling of Auto Insurance Data with Territory Design: A Rate Regulation Perspective," Mathematics, MDPI, vol. 11(2), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:334-:d:1029312
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/334/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/334/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michel Denuit & Arthur Charpentier & Julien Trufin, 2021. "Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning," Papers 2103.03635, arXiv.org, revised Jul 2021.
    2. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 485-497.
    3. Denuit, Michel & Charpentier , Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Reprints ISBA 2021049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Royce A. Francis & Srinivas Reddy Geedipally & Seth D. Guikema & Soma Sekhar Dhavala & Dominique Lord & Sarah LaRocca, 2012. "Characterizing the Performance of the Conway‐Maxwell Poisson Generalized Linear Model," Risk Analysis, John Wiley & Sons, vol. 32(1), pages 167-183, January.
    5. Shengkun Xie & Anna T. Lawniczak, 2018. "Estimating Major Risk Factor Relativities in Rate Filings Using Generalized Linear Models," IJFS, MDPI, vol. 6(4), pages 1-14, October.
    6. Ma, Yu-Luen & Zhu, Xiaoyu & Hu, Xianbiao & Chiu, Yi-Chang, 2018. "The use of context-sensitive insurance telematics data in auto insurance rate making," Transportation Research Part A: Policy and Practice, Elsevier, vol. 113(C), pages 243-258.
    7. Jean-Philippe Boucher & Roxane Turcotte, 2020. "A Longitudinal Analysis of the Impact of Distance Driven on the Probability of Car Accidents," Risks, MDPI, vol. 8(3), pages 1-19, September.
    8. Christopher Blier-Wong & Hélène Cossette & Luc Lamontagne & Etienne Marceau, 2020. "Machine Learning in P&C Insurance: A Review for Pricing and Reserving," Risks, MDPI, vol. 9(1), pages 1-26, December.
    9. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Discussion Papers ISBA 2021013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Kevin Kuo & Daniel Lupton, 2020. "Towards Explainability of Machine Learning Models in Insurance Pricing," Papers 2003.10674, arXiv.org.
    11. Banghee So & Jean-Philippe Boucher & Emiliano A. Valdez, 2021. "Synthetic Dataset Generation of Driver Telematics," Risks, MDPI, vol. 9(4), pages 1-19, March.
    12. Bian, Yiyang & Yang, Chen & Zhao, J. Leon & Liang, Liang, 2018. "Good drivers pay less: A study of usage-based vehicle insurance models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 107(C), pages 20-34.
    13. Montserrat Guillen & Jens Perch Nielsen & Ana M. Pérez-Marín & Valandis Elpidorou, 2020. "Can Automobile Insurance Telematics Predict the Risk of Near-Miss Events?," North American Actuarial Journal, Taylor & Francis Journals, vol. 24(1), pages 141-152, January.
    14. Nicholas Bett & Juma Kasozi & Daniel Ruturwa, 2022. "Temporal Clustering of the Causes of Death for Mortality Modelling," Risks, MDPI, vol. 10(5), pages 1-34, May.
    15. Guojun Gan & Emiliano A. Valdez, 2020. "Data Clustering with Actuarial Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 24(2), pages 168-186, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alinta Ann Wilson & Antonio Nehme & Alisha Dhyani & Khaled Mahbub, 2024. "A Comparison of Generalised Linear Modelling with Machine Learning Approaches for Predicting Loss Cost in Motor Insurance," Risks, MDPI, vol. 12(4), pages 1-29, March.
    2. Michał Strach & Krzysztof Różanowski & Jerzy Pietrucha & Jarosław Lewandowski, 2023. "Analysis of the Functionality of a Mobile Network of Sensors in a Construction Project Supervision System Based on Unmanned Aerial Vehicles," Sustainability, MDPI, vol. 16(1), pages 1-26, December.

    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. Yaojun Zhang & Lanpeng Ji & Georgios Aivaliotis & Charles Taylor, 2023. "Bayesian CART models for insurance claims frequency," Papers 2303.01923, arXiv.org, revised Dec 2023.
    2. Zhang, Yaojun & Ji, Lanpeng & Aivaliotis, Georgios & Taylor, Charles, 2024. "Bayesian CART models for insurance claims frequency," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 108-131.
    3. Denuit, Michel & Trufin, Julien, 2022. "Autocalibration by balance correction in nonlife insurance pricing," LIDAM Discussion Papers ISBA 2022041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Denuit, Michel & Trufin, Julien, 2022. "Tweedie dominance for autocalibrated predictors and Laplace transform order," LIDAM Discussion Papers ISBA 2022040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Mario V. Wuthrich & Johanna Ziegel, 2023. "Isotonic Recalibration under a Low Signal-to-Noise Ratio," Papers 2301.02692, arXiv.org.
    6. Yaojun Zhang & Lanpeng Ji & Georgios Aivaliotis & Charles C. Taylor, 2024. "Bayesian CART models for aggregate claim modeling," Papers 2409.01908, arXiv.org.
    7. Arthur Charpentier, 2022. "Quantifying fairness and discrimination in predictive models," Papers 2212.09868, arXiv.org.
    8. Fissler, Tobias & Merz, Michael & Wüthrich, Mario V., 2023. "Deep quantile and deep composite triplet regression," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 94-112.
    9. Denuit, Michel & Trufin, Julien & Verdebout, Thomas, 2021. "Testing for more positive expectation dependence with application to model comparison," LIDAM Discussion Papers ISBA 2021021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Montserrat Guillen & Jens Perch Nielsen & Ana M. Pérez‐Marín, 2021. "Near‐miss telematics in motor insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(3), pages 569-589, September.
    11. Francis Duval & Jean‐Philippe Boucher & Mathieu Pigeon, 2023. "Enhancing claim classification with feature extraction from anomaly‐detection‐derived routine and peculiarity profiles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 90(2), pages 421-458, June.
    12. Shengkun Xie & Rebecca Luo, 2022. "Measuring Variable Importance in Generalized Linear Models for Modeling Size of Loss Distributions," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    13. Meng, Shengwang & Gao, Yaqian & Huang, Yifan, 2022. "Actuarial intelligence in auto insurance: Claim frequency modeling with driving behavior features and improved boosted trees," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 115-127.
    14. Simon, Pierre-Alexandre & Trufin, Julien & Denuit, Michel, 2023. "Bivariate Poisson credibility model and bonus-malus scale for claim and near-claim events," LIDAM Discussion Papers ISBA 2023014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Omid Ghaffarpasand & Mark Burke & Louisa K. Osei & Helen Ursell & Sam Chapman & Francis D. Pope, 2022. "Vehicle Telematics for Safer, Cleaner and More Sustainable Urban Transport: A Review," Sustainability, MDPI, vol. 14(24), pages 1-20, December.
    16. Shengkun Xie, 2021. "Improving Explainability of Major Risk Factors in Artificial Neural Networks for Auto Insurance Rate Regulation," Risks, MDPI, vol. 9(7), pages 1-21, July.
    17. Qiong Bao & Hanrun Tang & Yongjun Shen, 2021. "Driving Behavior Based Relative Risk Evaluation Using a Nonparametric Optimization Method," IJERPH, MDPI, vol. 18(23), pages 1-15, November.
    18. Shengkun Xie & Chong Gan, 2023. "Estimating Territory Risk Relativity Using Generalized Linear Mixed Models and Fuzzy C -Means Clustering," Risks, MDPI, vol. 11(6), pages 1-20, May.
    19. Jan Reig Torra & Montserrat Guillen & Ana M. Pérez-Marín & Lorena Rey Gámez & Giselle Aguer, 2023. "Weather Conditions and Telematics Panel Data in Monthly Motor Insurance Claim Frequency Models," Risks, MDPI, vol. 11(3), pages 1-18, March.
    20. Alfiero, Simona & Battisti, Enrico & Ηadjielias, Elias, 2022. "Black box technology, usage-based insurance, and prediction of purchase behavior: Evidence from the auto insurance sector," Technological Forecasting and Social Change, Elsevier, vol. 183(C).

    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:2:p:334-:d:1029312. 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.