Nonlinear Optimization with Financial Applications

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1、NonlinearOptimizationwithFinancialApplicationsNonlinearOptimizationwithFinancialApplicationsMichaelBartholomew-BiggsUniversityofHertfordshireHatfield,EnglandKLUWERACADEMICPUBLISHERSBoston/DordrechtILondonLibraryofCongressCataloging-in-PublicationDataAC.I.P.Catalogu

2、erecordforthisbookisavailablefromtheLibraryofCongress.ISBN1-4020-8110-3e-ISBN0-387-24149-3Printedonacid-freepaper.O2005KluwerAcademicPublishersAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScien

3、ce+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknoworh

4、ereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,evenifthearenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.98765432

5、1SPIN11161363ContentsListofFiguresxi...ListofTablesXlllPreface1.PORTFOLIOOPTIMIZATION1Nonlinearoptimization2Portfolioreturnandrisk3Optimizingtwo-assetportfolios4Minimimumriskforthree-assetportfolios5Two-andthree-assetminimum-risksolutions6Aderivationoftheminimumris

6、kproblem7Maximumreturnproblems2.ONE-VARIABLEOPTIMIZATION1Optimalityconditions2Thebisectionmethod3Thesecantmethod4TheNewtonmethod5Methodsusingquadraticorcubicinterpolation6Solvingmaximum-returnproblems3.OPTIMALPORTFOLIOSWITHNASSETS1Introduction2Thebasicminimum-riskp

7、roblem3Minimumriskforspecifiedreturn4Themaximumreturnproblem4.UNCONSTRAINEDOPTIMIZATIONINNVARIABLES1Optimalityconditions2Visualisingproblemsinseveralvariables3Directsearchmethods4Optimizationsoftware&examples5.THESTEEPESTDESCENTMETHOD1Introduction2Linesearches3Conv

8、ergenceofthesteepestdescentmethod4Numericalresultswithsteepestdescent5Wolfe'sconvergencetheorem6Furtherresultswithsteepestdescent6.THENEWTONMETHO