FRÉCHET-HOEFFDING LOWER LIMIT COPULAS IN HIGHER DIMENSIONS

Abstract

Investigators have incorporated copula theories into their studies of multivariate dependency phenomena for many years. Copulas in general, which include the basic probability version as well as the Lévy and utility varieties, are enjoying a surge of popularity with applications to economics and finance. Ordinary copulas have a natural upper bound in all dimensions, the so-called Fréchet-Hoeffding limit, after the pioneering work of Wassily Hoeffding and, later, Maurice René Fréchet, working independently. Among the well-understood phenomena in the bivariate case is that a natural lower limit copula also exists. An extension of this copula, however, to the multidimensional case has not been forthcoming. This paper proposes such an extension of the lower limit distribution function and its copula, and examines some of their properties.