 A framework for optimization under ambiguityDavid Wozabal Annals of Operations Research, 2012, vol. 193, issue 1, 47 pages 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 Keywords: Robust optimization; Portfolio management; Difference of convex algorithm; Semi definite programming; Expected shortfall; Non-convex optimization (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:193:y:2012:i:1:p:21-47:10.1007/s10479-010-0812-0 Ordering information: This journal article can be ordered from DOI: 10.1007/s10479-010-0812-0 Access Statistics for this article Annals of Operations Research is currently edited by Endre Boros More articles in Annals of Operations Research from Springer |
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