The Construction of a class of bivariate copulas using the finite element method

Abstract

The definition of a copula function and the study of its properties are both not so easy tasks, as there is no general method to construct them. In this paper, we present a method that allows us to obtain a class of copulas as a solution to a boundary value problem. For this, we will use the finite element method. This method allows to set up, with the help of the principles inherited from the variational formulation or weak formulation, a discrete mathematical algorithm allowing to search for an approximate solution of a partial differential equation (or PDE) on a compact domain with conditions at the edges and/or in the interior of the compact.