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Approximations for probability distributions and stochastic optimization problems. (English) Zbl 1405.90093
Bertocchi, Marida (ed.) et al., Stochastic optimization methods in finance and energy. New financial products and energy market strategies. Selected papers based on the presentations at the spring school of stochastic programming, Bergamo, Italy, April 10–20, 2007, and the 11th international symposium on stochastic programming (SPXI), Vienna, Austria, August 27–31, 2007. New York, NY: Springer (ISBN 978-1-4419-9585-8/hbk; 978-1-4419-9586-5/ebook). International Series in Operations Research & Management Science 163, 343-387 (2011).
Summary: In this chapter, an overview of the scenario generation problem is given. After an introduction, the basic problem of measuring the distance between two single-period probability models is described in Section 15.2. Section 15.3 deals with finding good single-period scenarios based on the results of the first section. The distance concepts are extended to the multi-period situation in Section 15.4. Finally, Section 15.5 deals with the construction and reduction of scenario trees.
For the entire collection see [Zbl 1226.91004].

MSC:
90C15 Stochastic programming
60B10 Convergence of probability measures
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