Bounding separable recourse functions with limited distribution information (Q1178445)

For a function \(f(x)\), \(x=(x_ 1,\dots,x_ N)\in R^ N\), a separable approximation \(\nu(x)=\sum_{i=1}^ N\nu_ i(x_ i)\geq f(x)\) is developed. This approximation is used for finding an upper bound for the expectation \(Ef(x)=\int_ X f(x)Q(dx)\) where \(x\in X\subset R^ N\) is a random vector and the probability measure \(Q\in{\mathcal P}\), where \({\mathcal P}\) is a set of probability measures with certain properties. It is assumed that only first and second order moments of each \(x _ i\), \(i=1,2,\dots,N\), are known.