Stability and Scenario Trees for Multistage Stochastic Programs

Holger Heitsch () and Werner Römisch ()
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Holger Heitsch: Institute of Mathematics, Humboldt-University Berlin
Werner Römisch: Institute of Mathematics, Humboldt-University Berlin

Chapter Chapter 7 in Stochastic Programming, 2010, pp 139-164 from Springer

Abstract: Abstract By extending the stability analysis of Heitsch et al. (2006) for multistage stochastic programs we show that their (approximate) solution sets behave stable with respect to the sum of an $L_r$-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.

Keywords: Stochastic Program; Weak Topology; Scenario Tree; Spot Price; Spot Prex (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4419-1642-6_7

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DOI: 10.1007/978-1-4419-1642-6_7

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