Approximations and contamination bounds for probabilistic programs

Abstract

In this paper we aim at output analysis with respect to changes of the probability distribution for problems with probabilistic (chance) constraints. The perturbations are modeled via contamination of the initial probability distribution. Dependence of the set of solutions on the probability distributionrules out the straightforward construction of the convexity-based global contamination bounds for the perturbed optimal value function whereas localresults can be still obtained. To get global bounds we shall explore several approximations and reformulations of stochastic programs with probabilistic constraints by stochastic programs with suitably chosen recourse or penaltytype objectives and fixed constraints.