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Tail negative dependence and its applications for aggregate loss modeling

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  • Hua, Lei

Abstract

Tail order of copulas can be used to describe the strength of dependence in the tails of a joint distribution. When the value of tail order is larger than the dimension, it may lead to tail negative dependence. First, we prove results on conditions that lead to tail negative dependence for Archimedean copulas. Using the conditions, we construct new parametric copula families that possess upper tail negative dependence. Among them, a copula based on a scale mixture with a generalized gamma random variable (GGS copula) is useful for modeling asymmetric tail negative dependence. We propose mixed copula regression based on the GGS copula for aggregate loss modeling of a medical expenditure panel survey dataset. For this dataset, we find that there exists upper tail negative dependence between loss frequency and loss severity, and the introduction of tail negative dependence structures significantly improves the aggregate loss modeling.

Suggested Citation

  • Hua, Lei, 2015. "Tail negative dependence and its applications for aggregate loss modeling," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 135-145.
    • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:135-145
    DOI: 10.1016/j.insmatheco.2015.01.001
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    References listed on IDEAS

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    1. Lei Hua & Michelle Xia, 2014. "Assessing High-Risk Scenarios by Full-Range Tail Dependence Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(3), pages 363-378, July.
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    4. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
    5. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
    6. Yang, Xipei & Frees, Edward W. & Zhang, Zhengjun, 2011. "A generalized beta copula with applications in modeling multivariate long-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 265-284, September.
    7. Edward Frees & Jie Gao & Marjorie Rosenberg, 2011. "Predicting the Frequency and Amount of Health Care Expenditures," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(3), pages 377-392.
    8. Hua, Lei & Joe, Harry, 2012. "Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 492-503.
    9. Joe, Harry & Hu, Taizhong, 1996. "Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 240-265, May.
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    Cited by:

    1. Li, Haijun & Hua, Lei, 2015. "Higher order tail densities of copulas and hidden regular variation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 143-155.
    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. Michelle Xia, 2018. "Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression," Risks, MDPI, vol. 6(3), pages 1-16, August.
    4. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    5. Su, Jianxi & Hua, Lei, 2017. "A general approach to full-range tail dependence copulas," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 49-64.
    6. Karl Friedrich Siburg & Christopher Strothmann & Gregor Wei{ss}, 2022. "Comparing and quantifying tail dependence," Papers 2208.10319, arXiv.org.
    7. Hua, Lei & Joe, Harry, 2017. "Multivariate dependence modeling based on comonotonic factors," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 317-333.
    8. Salazar García, Juan Fernando & Guzmán Aguilar, Diana Sirley & Hoyos Nieto, Daniel Arturo, 2023. "Modelación de una prima de seguros mediante la aplicación de métodos actuariales, teoría de fallas y Black-Scholes en la salud en Colombia [Modelling of an insurance premium through the application," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 35(1), pages 330-359, June.
    9. Lee, Gee Y. & Shi, Peng, 2019. "A dependent frequency–severity approach to modeling longitudinal insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 115-129.
    10. Lei Hua, 2016. "A Note on Upper Tail Behavior of Liouville Copulas," Risks, MDPI, vol. 4(4), pages 1-10, November.
    11. Jaap Spreeuw, 2022. "The Copula Derived from the SAHARA Utility Function," Risks, MDPI, vol. 10(7), pages 1-10, June.
    12. Hua, Lei, 2017. "On a bivariate copula with both upper and lower full-range tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 94-104.

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