Stability of Ε-approximate Solutions to Convex Stochastic Programs∗

An analysis of convex stochastic programs is provided when the underlying probability distribution is subjected to (small) perturbations. It is shown, in particular, that ε-approximate solution sets of convex stochastic programs behave Lipschitz continuously with respect to certain distances of probability distributions that are generated by the relevant integrands. It is shown that these results apply to linear two-stage stochastic programs with random recourse. We discuss the consequences on associating Fortet–Mourier metrics to two-stage models and on the asymptotic behavior of empirical estimates of such models, respectively.