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2017-04-19Buch DOI: 10.18452/8455
Quantitative Stability Analysis for Minimax Distributionally Robust RiskOptimization
dc.contributor.authorPichler, Alois
dc.contributor.authorXu, Huifu
dc.contributor.editorHigle, Julie L.
dc.contributor.editorRömisch, Werner
dc.contributor.editorSen, Surrajeet
dc.date.accessioned2017-06-16T20:36:15Z
dc.date.available2017-06-16T20:36:15Z
dc.date.created2017-04-19
dc.date.issued2017-04-19
dc.date.submitted2017-04-12
dc.identifier.urihttp://edoc.hu-berlin.de/18452/9107
dc.description.abstractThis paper considers distributionally robust formulations of a two stage stochastic programmingproblem with the objective of minimizing a distortion risk of the minimal cost incurred at the secondstage.We carry out stability analysis by looking into variations of the ambiguity set under theWassersteinmetric, decision spaces at both stages and the support set of the random variables. In the case when itis risk neutral, the stability result is presented with the variation of the ambiguity set being measuredby generic metrics of ζ-structure, which provides a unified framework for quantitative stability analysisunder various metrics including total variation metric and Kantorovich metric. When the ambiguity set isstructured by a ζ-ball, we find that the Hausdorff distance between two ζ-balls is bounded by the distanceof their centres and difference of their radius. The findings allow us to strengthen some recent convergenceresults on distributionally robust optimization where the centre of the Wasserstein ball is constructed bythe empirical probability distribution.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectdistortion risk measureeng
dc.subject&zeta-balleng
dc.subjectWasserstein balleng
dc.subjectquantitative stability analysiseng
dc.subject.ddc510 Mathematik
dc.titleQuantitative Stability Analysis for Minimax Distributionally Robust RiskOptimization
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-100246239
dc.identifier.doihttp://dx.doi.org/10.18452/8455
local.edoc.container-titleStochastic Programming E-Print Series
local.edoc.pages22
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2017
local.edoc.container-issue3
local.edoc.container-erstkatid2936317-2

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