Evaluating and Approximating Expectations

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


The evaluation of the recourse function or the probability of satisfying a set of constraints can be quite complicated. This problem is basically one of numerical integration in high dimensions corresponding to the random variables. The general problem requires some form of approximation, such as quadrature formulas, which typically apply to smooth functions in low dimensions without using known convexity properties. In Section 8.1 of this chapter, we review some of these basic procedures, but note that stochastic programs often do not have differentiability as assumed in many numerical schemes but generally do have useful convexity properties.


Probability Measure Extreme Point Stochastic Program Moment Problem Probabilistic Constraint 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations