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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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    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. Guelman, Leo & Guillén, Montserrat & Pérez-Marín, Ana M., 2014. "A survey of personalized treatment models for pricing strategies in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 68-76.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    5. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    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.

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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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