06_Randomwalk

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1、ExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeFinancialEngineeringMartingaleandStoppingTimeHaiLanDept.ofManagementSciencesShanghaiJiaoTongUniversity.October23,2012H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingale

2、inFinanceApplicationsChangeofMeasureonBinomialTreeOutlineExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeH.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeLetY1;Y2;:

3、::beasequenceofindependent,identicalrandomvariablesandE(Yi)=0.LetFtbethenaturalltration.ThenthePtsequenceXt=j=1Yjisamartingale.H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeLetY1;Y2;:::beasequenceofindepe

4、ndent,identicalrandomvariablesandE(Yi)=0,Var(Yi)=2<1.LetFtbethenaturalP2ltration.ThenthesequencetY2tisamartingale.j=1jH.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTreeLetY1;Y2;:::beasequenceofindependen

5、t,identicalBernoulli-pPnrandomvariables,andletSn=j=1Yj.NotethatSnhasthebinomial-(n;p)distribution.Deneq2SnnZn=:pThenZnisamartingalerelativetotheusualltration.H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMeasureonBinomialTr

6、eeLetfXngbeamartingalerelativetotheltrationFnandlet':R!RbeaconvexfunctionsuchthatE'(Xn)<1foreachn0.ThenthesequencefZngdenedbyZn='(Xn)isasubmartingalerelativetotheltrationFn.H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartingaleinFinanceApplicationsChangeofMea

7、sureonBinomialTreeQuestionsWhenthereisnoarbitrageinthemarket,andmarketisecient,1.Canwebringadditionalfortunebydynamicallyre-balancingourportfolio?2.Canweavoidlossbyclearingourpositionbasedoninformationfrommarket?H.LanFinancialEngineeringExamplesofMartingaleImportanceofMartin

8、galeinFinanceApplicationsChangeofMeasureonBinomialTreeMartingaleTran