Optimal Control Models in Finance A New Computational Approach

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1、OPTIMALCONTROLMODELSINFINANCEAppliedOptimizationVolume95SeriesEditors:PanosM.PardalosUniversityofFlorida,U.S.A.DonaldW.HearnUniversityofFlorida,U.S.A.OPTIMALCONTROLMODELSINFINANCEANewComputationalApproachbyPINGCHENVictoriaUniversity,Melbourne,AustraliaSARDARM.N.ISLAMVictoriaUniversity,M

2、elbourne,AustraliaSpringereBookISBN:0-387-23570-1PrintISBN:0-387-23569-8©2005SpringerScience+BusinessMedia,Inc.Print©2005SpringerScience+BusinessMedia,Inc.BostonAllrightsreservedNopartofthiseBookmaybereproducedortransmittedinanyformorbyanymeans,electronic,mechanical,recording,orotherwis

3、e,withoutwrittenconsentfromthePublisherCreatedintheUnitedStatesofAmericaVisitSpringer'seBookstoreat:http://ebooks.springerlink.comandtheSpringerGlobalWebsiteOnlineat:http://www.springeronline.comContentsListofFiguresixListofTablesxiPrefacexiiiIntroductionxv1.OPTIMALCONTROLMODELS11AnOpti

4、malControlModelofFinance22(Karush)Kuhn-TuckerCondition43PontryaginTheorem64Bang-BangControl75SingularArc76IndifferencePrinciple87DifferentApproachestoOptimalControlProblems108Conclusion202.THESTVAPPROACHTOFINANCIALOPTIMALCONTROLMODELS211Introduction212Piecewise-linearTransformation213No

5、n-linearTimeScaleTransformation234AComputerSoftwarePackageUsedinthisStudy255AnOptimalControlProblemWhentheControlcanonlyTaketheValue0or1266ApproachestoBang-BangOptimalControlwithaCostofChangingControl277AnInvestmentPlanningModelandResults30viOPTIMALCONTROLMODELSINFINANCE8FinancialImplic

6、ationsandConclusion363.AFINANCIALOSCILLATORMODEL391Introduction392ControllingaDampedOscillatorinaFinancialModel403OscillatorTransformationoftheFinancialModel414ComputationalAlgorithm:TheSteps445FinancialControlPattern476ComputingtheFinancialModel:ResultsandAnalysis477FinancialInvestment

7、ImplicationsandConclusion894.ANOPTIMALCORPORATEFINANCINGMODEL911Introduction912ProblemDescription913AnalyticalSolution944PenaltyTerms985TransformationsfortheComputerSoftwarePackagefortheFinanceModel996ComputationalAlgorithmsfortheNon-linearOptimalControlProblem1017ComputingResu