A note on the use of copulas in chance-constrained programming

In this paper we are concentrated on a problem of linear chance-constrained programming where the constraint matrix is considered random with a known distribution of the matrix rows. The rows are not considered to be independent; instead, we make use of the copula notion to describe the dependence of the matrix rows. In particular, the distribution of the rows is driven by so-called Archimedean class of copulas. We provide a review of very basic properties of Archimedean copulas and describe how they can be used to transform the stochastic programming problem into a deterministic problem of second-order cone programming. Also the question of convexity of the problem is explored and importance of the selected class of copulas is commented. At the end of the paper, we provide a simple example to illustrate the concept used.