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Stability and Scenario Trees for Multistage Stochastic Programs

  • Holger Heitsch
  • Werner Römisch
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 150)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin, the BMBF under the grant 03SF0312E, and a grant of EDF – Electricité de France.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute of Mathematics, Humboldt-University BerlinBerlinGermany

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