Before revision:  In order to include this information in the computation of Value-at-Risk bounds, we establish a reduction principle that relates this problem to an optimization problem over a standard Fr\'echet class  . Second, we assume that the copula of \mathbf X is known on a subset of its domain, and finally we consider the case where the copula of \mathbf X lies in the vicinity of a reference copula as measured by a statistical distance.
After revision:  In order to include this information in the computation of Value-at-Risk bounds, we establish a reduction principle that relates this problem to an optimization problem over a standard Fr\'echet class , which can then be solved by means of the well-known standard bounds or the rearrangement algorithm . Second, we assume that the copula of \mathbf X is known on a subset of its domain, and finally we consider the case where the copula of \mathbf X lies in the vicinity of a reference copula as measured by a statistical distance.