03 Martingales June 2012

03 Martingales June 2012

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时间:2019-06-25

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1、StochasticCalculusandMartingales:APractitioner'sToolboxStochasticCalculusandMartingales:APractitioner'sToolboxCQF1/118StochasticCalculusandMartingales:APractitioner'sToolboxInthislecture......wewillexpandonthestochasticcalculuslecture(Lecture1.3)tointroducefurth

2、erprobabilisticconcepts:Itheprobabilisticuniverse;Isamplespace, ltrationandprobabilitymeasures;Iconditionalandunconditionalmeasures;IchangeofmeasureandtheRadonNicodymderivative;Ide nitionandpropertiesofmartingales.2/118StochasticCalculusandMartingales:APractiti

3、oner'sToolboxIntroductionIntroductionInthequantitative nanceliterature,mostarticleswritteninthepast10yearswillstartwiththewords:Let(;F;P)beaprobabilityspace..."Thetriple(;F;P),ormoreformally(;fFtg;F;P)iscalledaprobabilityspace,anditsinclusioninquantitative nanc

4、earticlesandbooksre ectstheincreasingin uenceofprobabilitytheoryandprobabilistsoverthesubject.Inthislecture,wewillgobeyondIt^ocalculustopresentamoreadvancedviewofprobabilitiesbasedlargelyonaclassofstochasticprocessescalledmartingales.3/118StochasticCalculusandMa

5、rtingales:APractitioner'sToolboxTheProbabilisticUniverseSection1:TheProbabilisticUniverseInthissection,wewilldiscussthetriple(;F;P),constitutedof1.thesamplespace;2.the ltrationF;3.theprobabilitymeasureP.Thistripleiscalledaprobabilityspaceanditrepresentsthefounda

6、tionsoftheprobabilisticuniverse.TheprobabilityspacegivestheirstructuretotheconceptsofBrownianmotion,It^ocalculusandstochasticdi erentialequationsthatyouarealreadyfamiliarwith.Whetheritisexplicitlymentionedornotinthearticlesorbooksyouread,theprobabilityspaceisalw

7、aystheresomewhereinthebackground.4/118StochasticCalculusandMartingales:APractitioner'sToolboxTheProbabilisticUniverse1.1-TheSampleSpaceAnevent,oroutcomeistheresultofagivenexperiment.Example:ObtainingaHead"inacointossexperimentisanevent.Usually,eventsaredenotedb

8、ytheGreeklowercapletteromega,!.5/118StochasticCalculusandMartingales:APractitioner'sToolboxTheProbabilisticUniverseThesamplespaceisthesetofallpossibleevents.Generally

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