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Multi-stage stochastic optimization: the distance between stochastic scenario processes

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  • Anna Timonina

Abstract

Approximation techniques are challenging, important and very often irreplaceable solution methods for multi-stage stochastic optimization programs. Applications for scenario process approximation include financial and investment planning, inventory control, energy production and trading, electricity generation planning, pension fund management, supply chain management and similar fields. In multi-stage stochastic optimization problems the amount of stage-wise available information is crucial. While some authors deal with filtration distances, in this paper we consider the concepts of nested distributions and their distances which allows to keep the setup purely distributional but at the same time to introduce information and information constraints. Also we introduce the distance between stochastic process and a tree and we generalize the concept of nested distance for the case of infinite trees, i.e. for the case of two stochastic processes given by their continuous distributions. We are making a step towards to a new method for distribution quantization that is the most suitable for multi-stage stochastic optimization programs as it takes into account both the stochastic process and the stage-wise information. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Anna Timonina, 2015. "Multi-stage stochastic optimization: the distance between stochastic scenario processes," Computational Management Science, Springer, vol. 12(1), pages 171-195, January.
    • Handle: RePEc:spr:comgts:v:12:y:2015:i:1:p:171-195
    DOI: 10.1007/s10287-013-0185-3
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    1. Georg Ch. Pflug & Alois Pichler, 2011. "Approximations for Probability Distributions and Stochastic Optimization Problems," International Series in Operations Research & Management Science, in: Marida Bertocchi & Giorgio Consigli & Michael A. H. Dempster (ed.), Stochastic Optimization Methods in Finance and Energy, edition 1, chapter 0, pages 343-387, Springer.
    2. Yuri Ermoliev & Tatiana Ermolieva & Guenther Fischer & Marek Makowski, 2010. "Extreme events, discounting and stochastic optimization," Annals of Operations Research, Springer, vol. 177(1), pages 9-19, June.
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    1. Markéta Horejšová & Sebastiano Vitali & Miloš Kopa & Vittorio Moriggia, 2020. "Evaluation of scenario reduction algorithms with nested distance," Computational Management Science, Springer, vol. 17(2), pages 241-275, June.

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