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A class of multivariate copulas with bivariate Frechet marginal copulas

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  • Yang, Jingping
  • Qi, Yongcheng
  • Wang, Ruodu

Abstract

In this paper, we present a class of multivariate copulas whose two-dimensional marginals belong to the family of bivariate Frechet copulas. The coordinates of a random vector distributed as one of these copulas are conditionally independent. We prove that these multivariate copulas are uniquely determined by their two-dimensional marginal copulas. Some other properties for these multivariate copulas are discussed as well. Two applications of these copulas in actuarial science are given.

Suggested Citation

  • Yang, Jingping & Qi, Yongcheng & Wang, Ruodu, 2009. "A class of multivariate copulas with bivariate Frechet marginal copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 139-147, August.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:139-147
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    References listed on IDEAS

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    1. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    2. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    3. Yang, Jingping & Cheng, Shihong & Zhang, Lihong, 2006. "Bivariate copula decomposition in terms of comonotonicity, countermonotonicity and independence," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 267-284, October.
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    Cited by:

    1. Janusz Milek, 2020. "Quantum Implementation of Risk Analysis-relevant Copulas," Papers 2002.07389, arXiv.org, revised Mar 2020.
    2. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    3. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.

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