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Subgroup analysis of zero-inflated Poisson regression model with applications to insurance data

Author

Listed:
  • Chen, Kun
  • Huang, Rui
  • Chan, Ngai Hang
  • Yau, Chun Yip
Abstract
Customized personal rate offering is of growing importance in the insurance industry. To achieve this, an important step is to identify subgroups of insureds from the corresponding heterogeneous claim frequency data. In this paper, a penalized Poisson regression approach for subgroup analysis in claim frequency data is proposed. Subjects are assumed to follow a zero-inflated Poisson regression model with group-specific intercepts, which capture group characteristics of claim frequency. A penalized likelihood function is derived and optimized to identify the group-specific intercepts and effects of individual covariates. To handle the challenges arising from the optimization of the penalized likelihood function, an alternating direction method of multipliers algorithm is developed and its convergence is established. Simulation studies and real applications are provided for illustrations.

Suggested Citation

  • Chen, Kun & Huang, Rui & Chan, Ngai Hang & Yau, Chun Yip, 2019. "Subgroup analysis of zero-inflated Poisson regression model with applications to insurance data," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 8-18.
    • Handle: RePEc:eee:insuma:v:86:y:2019:i:c:p:8-18
    DOI: 10.1016/j.insmatheco.2019.01.009
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    References listed on IDEAS

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    6. Partrat, Christian, 1994. "Compound model for two dependent kinds of claim," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 219-231, December.
    7. Yanlin Tang & Liya Xiang & Zhongyi Zhu, 2014. "Risk Factor Selection in Rate Making: EM Adaptive LASSO for Zero‐Inflated Poisson Regression Models," Risk Analysis, John Wiley & Sons, vol. 34(6), pages 1112-1127, June.
    8. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
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    Citations

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    Cited by:

    1. Marjan Qazvini, 2019. "On the Validation of Claims with Excess Zeros in Liability Insurance: A Comparative Study," Risks, MDPI, vol. 7(3), pages 1-17, June.
    2. Minwoo Kim & Himchan Jeong & Dipak Dey, 2022. "Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach," Risks, MDPI, vol. 10(3), pages 1-11, March.
    3. Bladt, Martin & Yslas, Jorge, 2023. "Robust claim frequency modeling through phase-type mixture-of-experts regression," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 1-22.
    4. Weirong Li & Wensheng Zhu, 2024. "Subgroup analysis with concave pairwise fusion penalty for ordinal response," Statistical Papers, Springer, vol. 65(6), pages 3327-3355, August.

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    More about this item

    Keywords

    ADMM algorithm; Car insurance data; Concave pairwise fusion penalty; Heterogeneity; Subgroup analysis;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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