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“Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution”

Author

Listed:
  • Catalina Bolancé

    (Research group–IREA. Av. Diagonal 696; 08034 Barcelona ,Spain.)

  • Raluca Vernic

    (Faculty of Mathematics and Informatics Ovidius University of Constanta; Bd Mamaia 124, 900527 Constanta, Romania.)

Abstract

Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals and incorporate various individual characteristics of the policyholders by means of explanatory variables. Since the data set was collected over a longer time period (10 years), we also added each individual’s exposure to risk. To estimate the parameters of the three Sarmanov distributions, we analyze a pseudo-maximumlikelihood method. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM.

Suggested Citation

  • Catalina Bolancé & Raluca Vernic, 2017. "“Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution”," IREA Working Papers 201718, University of Barcelona, Research Institute of Applied Economics, revised Oct 2017.
    • Handle: RePEc:ira:wpaper:201718
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    File URL: http://www.ub.edu/irea/working_papers/2017/201718.pdf
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    References listed on IDEAS

    as
    1. Shi, Peng & Valdez, Emiliano A., 2014. "Multivariate negative binomial models for insurance claim counts," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 18-29.
    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. Boucher, Jean-Philippe & Inoussa, Rofick, 2014. "A Posteriori Ratemaking With Panel Data," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 587-612, September.
    4. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2016. "Sarmanov family of multivariate distributions for bivariate dynamic claim counts model," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 120-133.
    5. Patrick L. Brockett & Linda L. Golden & Montserrat Guillen & Jens Perch Nielsen & Jan Parner & Ana Maria Perez‐Marin, 2008. "Survival Analysis of a Household Portfolio of Insurance Policies: How Much Time Do You Have to Stop Total Customer Defection?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 713-737, September.
    6. Bolancé, Catalina & Bahraoui, Zuhair & Artís, Manuel, 2014. "Quantifying the risk using copulae with nonparametric marginals," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 46-56.
    7. 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.
    8. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    9. Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multivariate counting distribution; Sarmanov distribution; Negative Binomial distribution; Generalized Linear Model; ML estimation algorithm. JEL classification: C51; G22.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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