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A Logistic Regression Based Auto Insurance Rate-Making Model Designed for the Insurance Rate Reform

Author

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  • Zhengmin Duan

    (College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China)

  • Yonglian Chang

    (College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China)

  • Qi Wang

    (College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China)

  • Tianyao Chen

    (College of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710000, China)

  • Qing Zhao

    (Lingnan College of Sun Yat-sen University, Guangzhou 510000, China)

Abstract

Using a generalized linear model to determine the claim frequency of auto insurance is a key ingredient in non-life insurance research. Among auto insurance rate-making models, there are very few considering auto types. Therefore, in this paper we are proposing a model that takes auto types into account by making an innovative use of the auto burden index. Based on this model and data from a Chinese insurance company, we built a clustering model that classifies auto insurance rates into three risk levels. The claim frequency and the claim costs are fitted to select a better loss distribution. Then the Logistic Regression model is employed to fit the claim frequency, with the auto burden index considered. Three key findings can be concluded from our study. First, more than 80% of the autos with an auto burden index of 20 or higher belong to the highest risk level. Secondly, the claim frequency is better fitted using the Poisson distribution, however the claim cost is better fitted using the Gamma distribution. Lastly, based on the AIC criterion, the claim frequency is more adequately represented by models that consider the auto burden index than those do not. It is believed that insurance policy recommendations that are based on Generalized linear models (GLM) can benefit from our findings.

Suggested Citation

  • Zhengmin Duan & Yonglian Chang & Qi Wang & Tianyao Chen & Qing Zhao, 2018. "A Logistic Regression Based Auto Insurance Rate-Making Model Designed for the Insurance Rate Reform," IJFS, MDPI, vol. 6(1), pages 1-16, February.
    • Handle: RePEc:gam:jijfss:v:6:y:2018:i:1:p:18-:d:130591
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Shengkun Xie, 2019. "Defining Geographical Rating Territories in Auto Insurance Regulation by Spatially Constrained Clustering," Risks, MDPI, vol. 7(2), pages 1-20, April.
    3. Erik Šoltés & Silvia Zelinová & Mária Bilíková, 2019. "General Linear Model: An Effective Tool For Analysis Of Claim Severity In Motor Third Party Liability Insurance," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 13-31, December.
    4. Šoltés Erik & Zelinová Silvia & Bilíková Mária, 2019. "General Linear Model: An Effective Tool For Analysis Of Claim Severity In Motor Third Party Liability Insurance," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 13-31, December.
    5. Leunglung Chan, 2018. "Editorial for Special Issue “Finance, Financial Risk Management and their Applications”," IJFS, MDPI, vol. 6(4), pages 1-3, October.
    6. Jennifer S. K. Chan & S. T. Boris Choy & Udi Makov & Ariel Shamir & Vered Shapovalov, 2022. "Variable Selection Algorithm for a Mixture of Poisson Regression for Handling Overdispersion in Claims Frequency Modeling Using Telematics Car Driving Data," Risks, MDPI, vol. 10(4), pages 1-10, April.

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