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Monte Carlo Methods

  • John R. BirgeEmail author
  • François Louveaux
Chapter
Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE)

Abstract

Each function value in a stochastic program can involve a multidimensional integral in extremely high dimensions. Because Monte Carlo simulation appears to offer the best possibilities for higher dimensions (see, e.g., Deák [1988] and Asmussen and Glynn [2007]), it seems to be the natural choice for use in stochastic programs. In this chapter, we describe some of the basic approaches built on sampling methods. The key feature is the use of statistical estimates to obtain confidence intervals on results. Some of the material uses probability measure theory which is necessary to develop the analytical results.

Keywords

Stochastic Program Importance Sampling Probabilistic Constraint Shaped Method Sample Average Approximation 
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.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Booth School of BusinessUniversity of ChicagoChicagoUSA
  2. 2.Department of Business AdministrationUniversity of NamurNamurBelgium

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