On Stability of Multistage Stochastic Programs

We study the quantitative stability of linear multistage stochastic programs under perturbations of the underlying stochastic processes. It is shown that the optimal values behave Lipschitz continuously with respect to an Lᵖ-distance. In order to establish continuity of the recourse function with respect to the current state of the stochastic process, we assume continuity of the conditional distributions in terms of a Fortet–Mourier metric. The main stability result holds for nonanticipative approximations of the underlying process and thus represents a rigorous justification of established discretization techniques.