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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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DOI

10.1016/0142-1123(93)90536-y

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ISSN

1573-2878

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Convergent Bounds for Stochastic Programs with Exp

Authors: D Kuhn
Publish Date: 2009/01/16
Volume: 141, Issue: 3, Pages: 597-618
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Abstract

This article describes a bounding approximation scheme for convex multistage stochastic programs MSP that constrain the conditional expectation of some decisiondependent random variables Expected value constraints of this type are useful for modelling a decision maker’s risk preferences but they may also arise as artifacts of stageaggregation We develop two finitedimensional approximate problems that provide bounds on the infinitedimensional original problem and we show that the gap between the bounds can be made smaller than any prescribed tolerance Moreover the solutions of the approximate MSPs give rise to a feasible policy for the original MSP and this policy’s optimality gap is shown to be smaller than the difference of the bounds The considered problem class comprises models with integrated chance constraints and conditional valueatrisk constraints No relatively complete recourse is assumed

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