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.
Bibliographical noteFunding 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.
- Bivariate Fréchet copulas
- Conditional independence
- Marginal copulas
- Multivariate copulas