On Stability of Multistage Stochastic Programs

We study quantitative stability of linear multistage stochastic programs under perturbations of the underlying stochastic processes. It is shown that the optimal values behave Lipschitz continuous with respect to an Lp-distance. Therefor, we have to make a crucial regularity assumption on the conditional distributions, that allows to establish continuity of the recourse function with respect to the current state of the stochastic process. The main stability result holds for nonanticipative discretizations of the underlying process and thus represents a rigorous justification of established discretization techniques. AMS 2000 subject classification: 90C15, 90C31