Stability of Multistage Stochastic Programs

Zusammenfassung

Many stochastic optimization problems of practical interest do not allow for an analytic solution, and numerical approaches require the underlying probability measure to have finite support. Whenever the initial probability measure does not meet these demands, it has to be approximated by an auxiliary measure. Thereby, it is reasonable to choose the approximating measure such that the optimal value and the set of optimal decisions of the auxiliary problem are close to those of the originial problem. Consequently, perturbation and stability analysis of stochastic programs is necessary for the development of reliable techniques for discretization and scenario reduction. While stability properties are well understood for non-dynamic chance constrained and two-stage problems, cf. the recent survey by Römisch (2003), it turned out that the multistage case is more intricate. Recently, the latter situation has been studied by a variety of authors, and thus the following references should not be considered to be exhaustive. Statistical bounds have been provided by Shapiro (2003a).