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时间:2019-08-04
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1、ExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeFinancialEngineeringMartingaleandStoppingTimeHaiLanDept.ofManagementSciencesShanghaiJiaoTongUniversity.October23,2012H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingale
2、inFinanceApplicationsChangeofMeasureonBinomialTreeOutlineExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeH.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeLetY1;Y2;:
3、::beasequenceofindependent,identicalrandomvariablesandE(Yi)=0.LetFtbethenaturalltration.ThenthePtsequenceXt=j=1Yjisamartingale.H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeLetY1;Y2;:::beasequenceofindepe
4、ndent,identicalrandomvariablesandE(Yi)=0,Var(Yi)=2<1.LetFtbethenaturalP2ltration.ThenthesequencetY 2tisamartingale.j=1jH.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeLetY1;Y2;:::beasequenceofindependen
5、t,identicalBernoulli-pPnrandomvariables,andletSn=j=1Yj.NotethatSnhasthebinomial-(n;p)distribution.Deneq2Sn nZn=:pThenZnisamartingalerelativetotheusualltration.H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTr
6、eeLetfXngbeamartingalerelativetotheltrationFnandlet':R!RbeaconvexfunctionsuchthatE'(Xn)<1foreachn0.ThenthesequencefZngdenedbyZn='(Xn)isasubmartingalerelativetotheltrationFn.H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMea
7、sureonBinomialTreeQuestionsWhenthereisnoarbitrageinthemarket,andmarketisecient,1.Canwebringadditionalfortunebydynamicallyre-balancingourportfolio?2.Canweavoidlossbyclearingourpositionbasedoninformationfrommarket?H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartin
8、galeinFinanceApplicationsChangeofMeasureonBinomialTreeMartingaleTran
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