Approximation and contamination bounds for probabilistic programs

Development of applicable robustness results for stochastic programs with probabilistic constraints is a demanding task. In this paper we follow the relatively simple ideas of output analysis based on the contamination technique and focus on construction of computable global bounds for the optimal value function. Dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of these concavity-based global bounds for the perturbed optimal value function whereas local results can still be obtained. Therefore we explore approximations and reformulations of stochastic programs with probabilistic constraints by stochastic programs with suitably chosen recourse or penalty-type objectives and fixed constraints. Contamination bounds constructed for these substitute problems may be then implemented within the output analysis for the original probabilistic program.