Explicit Bounds for the Distribution Function of the Sum of Dependent Normally Distributed Random Variables

Abstract

In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the important Frechet bounds the dependence structure is not restricted to any specific type. Numerical illustrations are provided to assess the quality of the derived bounds.Comment: Keywords: Dependent RVs, Copulas, Frechet Bound