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1、OptimizationMethodsinFinanceGerardCornuejolsRehaTut?unc?u?CarnegieMellonUniversity,Pittsburgh,PA15213USAJanuary20062ForewordOptimizationmodelsplayanincreasinglyimportantrolein nancialde-cisions.Manycomputational nanceproblemsrangingfromassetallocationt
2、oriskmanagement,fromoptionpricingtomodelcalibrationcanbesolvedecientlyusingmodernoptimizationtechniques.Thiscoursediscussessev-eralclassesofoptimizationproblems(includinglinear,quadratic,integer,dynamic,stochastic,conic,androbustprogramming)encountere
3、din nan-cialmodels.Foreachproblemclass,afterintroducingtherelevanttheory(optimalityconditions,duality,etc.)andecientsolutionmethods,wedis-cussseveralproblemsofmathematical nancethatcanbemodeledwithinthisproblemclass.Inadditiontoclassicalandwell-knownm
4、odelssuchasMarkowitz'mean-varianceoptimizationmodelwepresentsomeneweroptimizationmodelsforavarietyof nancialproblems.AcknowledgementsThisbookhasitsoriginsincoursestaughtatCarnegieMellonUniversityintheMastersprograminComputationalFinanceandintheMBAprogr
5、amattheTepperSchoolofBusiness(GerardCornuejols),andattheTokyoIn-stituteofTechnology,Japan,andtheUniversityofCoimbra,Portugal(RehaTut?unc?u).?Wethanktheattendantsofthesecoursesfortheirfeedbackandformanystimulatingdiscussions.Wewouldalsoliketothankthec
6、olleagueswhoprovidedtheinitialimpetusforthisproject,especiallyMichaelTrick,JohnHooker,SanjaySrivastava,RickGreen,YanjunLi,LusVicenteandMasakazuKojima.VariousdraftsofthisbookwereexperimentedwithinclassbyJavierPena,~FrancoisMargot,MiroslavKaramanovand
7、KathieCameron,andwethankthemfortheircomments.Contents1Introduction91.1OptimizationProblems......................91.1.1LinearandNonlinearProgramming..........101.1.2QuadraticProgramming.................111.1.3ConicOptimization...................121.1.4I
8、ntegerProgramming..................121.1.5DynamicProgramming.................131.2OptimizationwithDataUncertainty..............131.2.1StochasticProgramming.................131.2.2RobustOptimization...................141.3FinancialMathem
