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Bound-Based Decision Rules in Multistage Stochastic Programming

Daniel Kuhn, Panos Parpas & Berç Rustem

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abstract We study bounding approximations for a multistage stochastic program with expected value constraints. Two simpler approximate stochastic programs, which provide upper and lower bounds on the original problem, are obtained by replacing the original stochastic data process by finitely supported approximate processes. We model the original and approximate processes as dependent random vectors on a joint probability space. This probabilistic coupling allows us to transform the optimal solution of the upper bounding problem to a near-optimal decision rule for the original problem. Unlike the scenario tree based solutions of the bounding problems, the resulting decision rule is implementable in all decision stages, i. e., there is no need for dynamic reoptimization during the planning period. Our approach is illustrated with a mean-risk portfolio optimization model.
   
type journal paper
   
keywords stochastic programming, bounds, decision rules, expected value constraints, portfolio optimization
   
language English
kind of paper journal article
date of appearance 1-5-2008
journal Kybernetika
publisher Institute of Information Theory and Automation of the Academy of Sciences of the Czech Republic (Prague)
ISSN 0023-5954
number of issue 44(2)
page(s) 34-150
review double-blind review
   
citation Kuhn, D., Parpas, P., & Rustem, B. (2008). Bound-Based Decision Rules in Multistage Stochastic Programming. Kybernetika(44(2)), 34-150.