A class of multivariate copulas with bivariate Fréchet marginal copulas

Jingping Yang; Yongcheng Qi; Ruodu Wang

doi:10.1016/j.insmatheco.2009.05.007

A class of multivariate copulas with bivariate Fréchet marginal copulas

Jingping Yang, Yongcheng Qi, Ruodu Wang

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

In this paper, we present a class of multivariate copulas whose two-dimensional marginals belong to the family of bivariate Fréchet 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.

Original language	English (US)
Pages (from-to)	139-147
Number of pages	9
Journal	Insurance: Mathematics and Economics
Volume	45
Issue number	1
DOIs	https://doi.org/10.1016/j.insmatheco.2009.05.007
State	Published - Aug 2009

Bibliographical note

Funding Information:
The authors thank two reviewers for their constructive suggestions which have led to much improvement on the paper. Yang’s research was supported by the National Basic Research Program (973 Program) of China (2007CB814905) and NSFC (10871008), and Qi’s research was supported by NSF grant DMS 0604176.

Keywords

Bivariate Fréchet copulas
Conditional independence
Marginal copulas
Multivariate copulas

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10.1016/j.insmatheco.2009.05.007

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abstract = "In this paper, we present a class of multivariate copulas whose two-dimensional marginals belong to the family of bivariate Fr{\'e}chet 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.",

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author = "Jingping Yang and Yongcheng Qi and Ruodu Wang",

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AU - Qi, Yongcheng

AU - Wang, Ruodu

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N2 - In this paper, we present a class of multivariate copulas whose two-dimensional marginals belong to the family of bivariate Fréchet 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.

AB - In this paper, we present a class of multivariate copulas whose two-dimensional marginals belong to the family of bivariate Fréchet 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.

KW - Bivariate Fréchet copulas

KW - Conditional independence

KW - Marginal copulas

KW - Multivariate copulas

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A class of multivariate copulas with bivariate Fréchet marginal copulas

Abstract

Bibliographical note

Keywords

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