quantitative stability for scenario-based stochastic programs

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1、QUANTITATIVESTABILITYFORSCENARIO-BASEDSTOCHASTICPROGRAMSJitkaDupacovaDepartmentofProbabilityandMathematicalStatistics,CharlesUniversitySokolovska83,18675Prague,CzechRepublice-mail:dupacova@karlin.m.cuni.czWernerRomischInstituteofMathematics,HumboldtUniversity,Unterd

2、enLinden6,D-10099Berlin,Germanye-mail:romisch@mathematik.hu-berlin.de1Abstractf:X!Ragivenfunction,denote'(P)=infEf(x;!)(2)PGeneralquantitativestabilityresultsforstochasticpro-x2Xgramsareformulatedintermsofprobabilitymetrics,spec-theoptimalvalueandiedtoscenario-basedst

3、ochasticprogramsandappliedtoabondportfoliomanagementproblem.(P)=argminEf(x;!)fx2Xjf(x;P)='(P)g(3)Px2XAMSclassication:90C15,90C31,60K30,90C08Keywords:Probabilitymetrics,stochasticprograms,sta-thesolutionset.Toadaptthegeneralquantitativesta-bilitywrt.probabilitymeasure,r

4、andomrecourse,discretebilityapproachesmeanstoselectametricdistancedofdistributions,applicationprobabilitymeasureswhichissuitablefromthepointofviewofthestructureoftheconsideredstochasticpro-gramand/oroftheparticulartypeofapproximationof1INTRODUCTIONprobabilitymeasurePfor

5、togetaLipschitz(orHolder)propertyoftheoptimalvalueStabilityandsensitivitystudiesforstochasticprogramshavebeenmotivatedbyanincompleteinformationabout00d(P;P)<)j'(P)?'(P)j

6、dpossiblyalsoaLipschitz(orHolder)propertyofthevariousdiscretizationandapproximationschemesneededHausdordistanceofthecorrespondingsolutionsetswithinconnectionwiththedevelopmentandevaluationofal-respecttoperturbationsofPmeasuredbyd;naturally,gorithms.Thesolvedreallifesto

7、chasticprogramsaretheLipschitz(orHolder)constantsdependonthechosenverycomplex;innumericalprocedures,oneusestheirspe-metricd.cicstructureandisinterestedinrobustsolutions:SmallTherstresultsconcerningtheoptimalvaluecanbechangesintheinput(inourcasemainlyperturbationsfound

8、in[12].Specialassumptionsareneededfortoex-oftheprobabilitymeasure)aresupposedtocauseonlytendtheseresultstotheo