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Stability and Scenario Trees for Multistage Stochastic Programs

In: Stochastic Programming

Author

Listed:
  • Holger Heitsch

    (Institute of Mathematics, Humboldt-University Berlin)

  • Werner Römisch

    (Institute of Mathematics, Humboldt-University Berlin)

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.

Suggested Citation

  • Holger Heitsch & Werner Römisch, 2010. "Stability and Scenario Trees for Multistage Stochastic Programs," International Series in Operations Research & Management Science, in: Gerd Infanger (ed.), Stochastic Programming, chapter 0, pages 139-164, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-1642-6_7
    DOI: 10.1007/978-1-4419-1642-6_7
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