A class of multivariate copulas with bivariate Fréchet marginal copulas

The complete mixability and convex minimization problems with monotone marginal densities

“…X 1 , X 2 and X 3 are negatively correlated with copula C (1,2,3) in [22] (i.e. the corresponding uniform random variables U 1 , U 2 and U 3 in (23) satisfy U 1 = 1 − U 3 and U 2 is independent of U 1 and U 3 ).…”

Bernoulli and tail-dependence compatibility

“…Introduction. The problem of how to construct a bivariate random vector (X 1 , X 2 ) with log-normal marginals X 1 ∼ LN(0, 1), X 2 ∼ LN(0, 16) and correlation coefficient Cor(X 1 , X 2 ) = 0.5 is well known in the history of dependence modeling, partially because of its relevance to risk management practice. The short answer is: There is no such model; see Embrechts et al [6] who studied these kinds of problems in terms of copulas.…”

Pricing k th realization derivatives and collateralized debt obligation with multivariate Fréchet copula

“…This paper proposed to use the multivariate Fréchet copula family presented in [13] for pricing multivariate financial instruments with payments depending on the k th realization of the underlying assets. The theoretical advantage by using the multivariate Fréchet copula was presented.…”

“…The multivariate Fréchet copula family has been introduced by Yang et al [13]. Both Assumptions A and B have their practical implications when modeling risks in insurance and finance.…”

“…The multivariate Fréchet copula family was presented by Yang et al [13]. The multivariate Fréchet copula is based on the widely accepted conditional independence assumption and all of its 2-dimensional marginal copulas are the bivariate Fréchet copulas which have very clear probability structure and financial interpretation [12].…”