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The Applications of Generalized Poisson Regression Models to Insurance Claim Data

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  • Pouya Faroughi

    (School of Mathematical and Computational Sciences, University of Prince Edward Island, Charlottetown, PE C1A 4P3, Canada)

  • Shu Li

    (Department of Statistical and Actuarial Sciences, Western University, London, ON N6A 5B7, Canada)

  • Jiandong Ren

    (Department of Statistical and Actuarial Sciences, Western University, London, ON N6A 5B7, Canada)

Abstract

Predictive modeling has been widely used for insurance rate making. In this paper, we focus on insurance claim count data and address their common issues with more flexible modeling techniques. In particular, we study the zero-inflated and hurdle-generalized Poisson and negative binomial distributions in a functional form for modeling insurance claim count data. It is shown that these models are useful in addressing the problem of excess zeros and over-dispersion of the claim count variable. In addition, we show that including the exposure as a covariate in both the zero and the count part of the model is an effective approach to incorporating exposure information in zero-inflated and hurdle models. We illustrate the effectiveness and versatility of the introduced models using three real datasets. The results suggest their promising applications in insurance risk classification and beyond.

Suggested Citation

  • Pouya Faroughi & Shu Li & Jiandong Ren, 2023. "The Applications of Generalized Poisson Regression Models to Insurance Claim Data," Risks, MDPI, vol. 11(12), pages 1-17, December.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:12:p:213-:d:1296011
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    References listed on IDEAS

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    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
    2. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    3. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    4. Weiren Wang & Felix Famoye, 1997. "Modeling household fertility decisions with generalized Poisson regression," Journal of Population Economics, Springer;European Society for Population Economics, vol. 10(3), pages 273-283.
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