On Stability of Multistage Stochastic Programs

Abstract

We study quantitative stability of linear multistage stochastic programs underperturbations of the underlying stochastic processes. It is shown that the optimalvalues behave Lipschitz continuous with respect to an $L_p$-distance. Therefore, wehave to make a crucial regularity assumption on the conditional distributions, thatallows to establish continuity of the recourse function with respect to the currentstate of the stochastic process. The main stability result holds for nonanticipativediscretizations of the underlying process and thus represents a rigorous justificationof established discretization techniques.