基于MGARCH模型的情景树生成算法.pdf

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1、CHINESEJoURNALJune2014oFENGINEERINGMrHEMATICSVb1．31No．3doi：10．3969／j．issn．1005—3085．2014．03．013ArticleID：1005--3085(2014)03-0435．．19ScenarioTreeGenerationAlgorithmsunderMGARCHMOdels冰XUDao—baoI．CHENZhi—ping2．YUGuan3(1一NanjingResearchInstituteofElectronicsTechnology,Nanjing210039；2一SchoolofMathematic

2、sandStatistics，Xi’anJiaotongUniversity,Xi’an710049；3一SchoolofEconomic＆Management，NorthwestUniversity,Xi’an710127)Abstract：Thequalityofmulti—stagestochasticoptimizationmodelsdependsheavilyonthequalityoftheunderlyingscenariotreetodescribetheuncertainenvironment．Ex-istingscenariogenerationalgorithmsar

3、eimprovedfromthefollowingaspects：toproperlyreflectvariationsinhigherordermomentsoftheunderlyingrandomdataprocess，weproposeanewsimulationapproachforscenariogenerationundertheMGARCHmodel；toimprovethecurrentsequentialoptimizationscenariogenera-tionmethod，theMGARCHmodelisusedtorecursivelyestimatecentra

4、lmomentsofthestochasticdataprocess，andanewhybridintelligentalgorithmisdesignedtosolvenon--convexprogrammingproblemsencounteredduringthesequentialopti—-mizationprocess，derivedfromwhichisaneficientnew-typesequentialoptimizationmethodforgeneralmultistagescenariotreegenerationunderMGARCHmodels；finally,

5、numericalresultswithtradedatafromChineseandAmericanstockmarketsillustratethepracticality，flexibilityandeficiencyofouralgorithms．Keywords：scenario；treestructure；scenariogeneration；simulation；sequentialoptimizationClassification：AMS(2000)90C15CLCnumber：O221．5；O212．2Documentcode：A1IntroductionInavarie

6、tyofapplicationssuchasfinancialoptimization，electricityportfolioman—agement，large—scaleproductionsystemdesign，oneisoftenfacedwithmultistagese—quentialdecisionproblemsinrandomenvironment．Forthesecomplexdecisionprob—lemsunderuncertainty,anessentialpointtomaketherelevantdecisionmodelpracticalandsolvab

7、leishowtoprovideacoherentandfiniterepresentationoftheinvolvedran-domdataprocess．Thisiscalledscenariogenerationintheliterature．andeachcoherentsetofparametervaluesovertheplanninghorizoncorrespondstoascenario．