Stability and scenario trees for multistage stochastic programs

By extending the stability analysis of [20] for multistage stochastic programs we show that their (approximate) solution sets behave stable with respect to the sum of an Lr-distance and a filtration distance. Based on such stability results we suggest a scenario tree generation method for the (multivariate) stochastic input process. It starts with an initial scenario set and consists of a recursive deletion and branching procedure which is controlled by bounding the approximation error. Some numerical experience for generating scenario trees in electricity portfolio management is reported.