Before revision: We derive bounds on the distribution function, therefore also on the Value-at-Risk, of \varphi(\mathbf X) where \varphi is an aggregation function and \mathbf X = (X_1, ... \dots ,X_d) is a random vector with known marginal distributions and partially known dependence structure.
After revision: We derive bounds on the distribution function, therefore also on the Value-at-Risk, of \varphi(\mathbf X) where \varphi is an aggregation function and \mathbf X = (X_1, \dots ,X_d) is a random vector with known marginal distributions and partially known dependence structure.