A framework for optimization under ambiguity

In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure P̂ enables the construction of non-parametric ambiguity sets as Kantorovich balls around P̂ . The resulting robustified problems are infinite optimization problems and can therefore not be solved computationally. To solve these problems numerically, equivalent formulations as finite dimensional non-convex, semi definite saddle point problems are proposed. Finally an application from portfolio selection is studied for which methods to solve the robust counterpart problems explicitly are proposed and numerical results for sample problems are computed.