  This paper introduces vector copulas associated with multivariate
distributions with given multivariate marginals, based on the theory of measure
transportation, and establishes a vector version of Sklar's theorem. The latter
provides a theoretical justification for the use of vector copulas to
characterize nonlinear or rank dependence between a finite number of random
vectors (robust to within vector dependence), and to construct multivariate
distributions with any given non overlapping multivariate marginals. We
construct Elliptical and Kendall families of vector copulas, derive their
densities, and present algorithms to generate data from them. The use of vector
copulas is illustrated with a stylized analysis of international financial
contagion.
