Scenario tree modelling for multistage stochastic programs

Abstract

An important issue for solving multistage stochastic programs consists inthe approximate representation of the (multivariate) stochastic input process inthe form of a scenario tree. In this paper, forward and backward approachesare developed for generating scenario trees out of an initial fan of individualscenarios. Both approaches are motivated by the recent stability result in [15]for optimal values of multistage stochastic programs. They are based on upperbounds for the two relevant ingredients of the stability estimate, namely, theprobabilistic and the filtration distance, respectively. These bounds allow tocontrol the process of recursive scenario reduction [13] and branching. Numericalexperience is reported for constructing multivariate scenario trees in electricityportfolio management.