資源描述:
《quantitative stability for scenario-based stochastic programs》由會員上傳分享,免費在線閱讀,更多相關內容在教育資源-天天文庫。
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-theoptimalvalueandiedtoscenario-basedst
3、ochasticprogramsandappliedtoabondportfoliomanagementproblem.(P)=argminEf(x;!)fx2Xjf(x;P)='(P)g(3)Px2XAMSclassication: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)j6、dpossiblyalsoaLipschitz(orHolder)propertyofthevariousdiscretizationandapproximationschemesneededHausdordistanceofthecorrespondingsolutionsetswithinconnectionwiththedevelopmentandevaluationofal-respecttoperturbationsofPmeasuredbyd;naturally,gorithms.Thesolvedreallifesto
7、chasticprogramsaretheLipschitz(orHolder)constantsdependonthechosenverycomplex;innumericalprocedures,oneusestheirspe-metricd.cicstructureandisinterestedinrobustsolutions:SmallTherstresultsconcerningtheoptimalvaluecanbechangesintheinput(inourcasemainlyperturbationsfound
8、in[12].Specialassumptionsareneededfortoex-oftheprobabilitymeasure)aresupposedtocauseonlytendtheseresultstotheo