Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 142, Issue 2, Pages 399-416Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-009-9523-6
Keywords
Chance constraints; Sample average approximation; Portfolio selection
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We study sample approximations of chance constrained problems. In particular, we consider the sample average approximation (SAA) approach and discuss the convergence properties of the resulting problem. We discuss how one can use the SAA method to obtain good candidate solutions for chance constrained problems. Numerical experiments are performed to correctly tune the parameters involved in the SAA. In addition, we present a method for constructing statistical lower bounds for the optimal value of the considered problem and discuss how one should tune the underlying parameters. We apply the SAA to two chance constrained problems. The first is a linear portfolio selection problem with returns following a multivariate lognormal distribution. The second is a joint chance constrained version of a simple blending problem.
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