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On the Type I multivariate zero-truncated hurdle model with applications in health insurance

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  • Zhang, Pengcheng
  • Calderin, Enrique
  • Li, Shuanming
  • Wu, Xueyuan

Abstract

In the general insurance modeling literature, there has been a lot of work based on univariate zero-truncated models, but little has been done in the multivariate zero-truncation cases, for instance a line of insurance business with various classes of policies. There are three types of zero-truncation in the multivariate setting: only records with all zeros are missing, zero counts for one or some classes are missing, or zeros are completely missing for all classes. In this paper, we focus on the first case, the so-called Type I zero-truncation, and a new multivariate zero-truncated hurdle model is developed to study it. The key idea of developing such a model is to identify a stochastic representation for the underlying random variables, which enables us to use the EM algorithm to simplify the estimation procedure. This model is used to analyze a health insurance claims dataset that contains claim counts from different categories of claims without common zero observations.

Suggested Citation

  • Zhang, Pengcheng & Calderin, Enrique & Li, Shuanming & Wu, Xueyuan, 2020. "On the Type I multivariate zero-truncated hurdle model with applications in health insurance," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 35-45.
    • Handle: RePEc:eee:insuma:v:90:y:2020:i:c:p:35-45
    DOI: 10.1016/j.insmatheco.2019.10.010
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    References listed on IDEAS

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    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
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    3. Karlis, Dimitris, 2005. "EM Algorithm for Mixed Poisson and Other Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 3-24, May.
    4. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    5. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
    6. Ch. Charalambides, 1984. "Minimum variance unbiased estimation for the zero class truncated bivariate poisson and logarithmic series distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 115-123, December.
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    Cited by:

    1. 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.
    2. Emilio Gómez-Déniz & Enrique Calderín-Ojeda, 2021. "A Priori Ratemaking Selection Using Multivariate Regression Models Allowing Different Coverages in Auto Insurance," Risks, MDPI, vol. 9(7), pages 1-18, July.

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