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A framework for optimization under ambiguity

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  • David Wozabal

Abstract

In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure $\hat {P}$ enables the construction of non-parametric ambiguity sets as Kantorovich balls around $\hat{P}$ . The original stochastic optimization problems are robustified by a worst case approach with respect to these ambiguity sets. The resulting problems are infinite optimization problems and can therefore not be solved computationally by straightforward methods. To nevertheless solve the robustified problems numerically, equivalent formulations as finite dimensional non-convex, semi definite saddle point problems are proposed. Finally an application from portfolio selection is studied for which methods to solve the robust counterpart problems explicitly are proposed and numerical results for sample problems are computed. Copyright Springer Science+Business Media, LLC 2012

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  • David Wozabal, 2012. "A framework for optimization under ambiguity," Annals of Operations Research, Springer, vol. 193(1), pages 21-47, March.
    • Handle: RePEc:spr:annopr:v:193:y:2012:i:1:p:21-47:10.1007/s10479-010-0812-0
    DOI: 10.1007/s10479-010-0812-0
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