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

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  • Bolancé, Catalina
  • Vernic, Raluca

Abstract

Starting from the question: What is the accident risk of an insured individual?, we consider that the customer has contracted policies in different insurance lines: motor and home. Three models based on the multivariate Sarmanov distribution are analyzed. Driven by a real data set that takes into account three types of accident risks, two for motor and one for home, three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals are considered and fitted to the data. To estimate the parameters of these three models, we discuss a method for approaching the maximum likelihood (ML) estimators. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM and with elliptical copula based models.

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  • Bolancé, Catalina & Vernic, Raluca, 2019. "Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 89-103.
    • Handle: RePEc:eee:insuma:v:85:y:2019:i:c:p:89-103
    DOI: 10.1016/j.insmatheco.2019.01.001
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    References listed on IDEAS

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    1. 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.
    2. Boucher, Jean-Philippe & Inoussa, Rofick, 2014. "A Posteriori Ratemaking With Panel Data," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 587-612, September.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Bolancé, Catalina & Guillén, Montserrat & Pinquet, Jean, 2008. "On the link between credibility and frequency premium," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 209-213, October.
    9. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
    10. 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.
    11. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
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    Cited by:

    1. Catalina Bolancé & Raluca Vernic, 2020. "Frequency and Severity Dependence in the Collective Risk Model: An Approach Based on Sarmanov Distribution," Mathematics, MDPI, vol. 8(9), pages 1-17, August.
    2. Vernic, Raluca & Bolancé, Catalina & Alemany, Ramon, 2022. "Sarmanov distribution for modeling dependence between the frequency and the average severity of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 111-125.
    3. Khouzeima Moutanabbir & Hassan Abdelrahman, 2022. "Bivariate Sarmanov Phase-Type Distributions for Joint Lifetimes Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1093-1118, June.
    4. Ramon Alemany & Catalina Bolancé & Roberto Rodrigo & Raluca Vernic, 2020. "Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence—An Application to Model Claim Frequency and Optimal Transformed Average Severity," Mathematics, MDPI, vol. 9(1), pages 1-18, December.
    5. George Tzougas & Despoina Makariou, 2022. "The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(4), pages 401-417, December.
    6. Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    7. Zezhun Chen & Angelos Dassios & George Tzougas, 2023. "Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression," Computational Statistics, Springer, vol. 38(2), pages 955-977, June.
    8. Catalina Bolancé & Montserrat Guillen & Albert Pitarque, 2020. "A Sarmanov Distribution with Beta Marginals: An Application to Motor Insurance Pricing," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    9. Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2023. "EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects," LSE Research Online Documents on Economics 118826, London School of Economics and Political Science, LSE Library.

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