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2005-11-07Buch DOI: 10.18452/2661
Quantitative stability in stochastic programming: The method of probability metrics
dc.contributor.authorRachev, Svetlozar T.
dc.contributor.authorRömisch, Werner
dc.date.accessioned2017-06-15T17:53:45Z
dc.date.available2017-06-15T17:53:45Z
dc.date.created2005-11-07
dc.date.issued2005-11-07
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3313
dc.description.abstractQuantitative stability of optimal values and solution sets to stochastic programming problems is studied when the underlying probability distribution varies in some metric space of probability measures. We give conditions that imply that a stochastic program behaves stable with respect to a minimal information (m.i.) probability metric that is naturally associated with the data of the program. Canonical metrics bounding the m.i. metric are derived for specific models, namely for linear two-stage, mixed-integer two-stage and chance constrained models. The corresponding quantitative stability results as well as some consequences for asymptotic properties of empirical approximations extend earlier results in this direction. In particular, rates of convergence in probability are derived under metric entropy conditions. Finally, we study stability properties of stable investment portfolios having minimal risk with respect to the spectral measure and stability index of the underlying stable probability distribution.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.subjectquantitative stabilityeng
dc.subjectStochastic programmingeng
dc.subjectprobability metricseng
dc.subjectFortet-Mourier metricseng
dc.subjectempirical approximationseng
dc.subjecttwo-stage modelseng
dc.subjectchance constrained modelseng
dc.subjectstable portfolio modelseng
dc.subject.ddc510 Mathematik
dc.titleQuantitative stability in stochastic programming: The method of probability metrics
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10052965
dc.identifier.doihttp://dx.doi.org/10.18452/2661
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages29
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2000
local.edoc.container-issue22
local.edoc.container-year2000
local.edoc.container-erstkatid2075199-0

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