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ID:39149394
大小:594.94 KB
页数:119页
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;Idenitionandpropertiesofmartingales.2/118StochasticCalculusandMartingales:APractiti
3、oner'sToolboxIntroductionIntroductionInthequantitativenanceliterature,mostarticleswritteninthepast10yearswillstartwiththewords:Let(;F;P)beaprobabilityspace..."Thetriple(;F;P),ormoreformally(;fFtg;F;P)iscalledaprobabilityspace,anditsinclusioninquantitativenanc
4、earticlesandbooksre ectstheincreasingin uenceofprobabilitytheoryandprobabilistsoverthesubject.Inthislecture,wewillgobeyondIt^ocalculustopresentamoreadvancedviewofprobabilitiesbasedlargelyonaclassofstochasticprocessescalledmartingales.3/118StochasticCalculusandMa
5、rtingales:APractitioner'sToolboxTheProbabilisticUniverseSection1:TheProbabilisticUniverseInthissection,wewilldiscussthetriple(;F;P),constitutedof1.thesamplespace;2.theltrationF;3.theprobabilitymeasureP.Thistripleiscalledaprobabilityspaceanditrepresentsthefounda
6、tionsoftheprobabilisticuniverse.TheprobabilityspacegivestheirstructuretotheconceptsofBrownianmotion,It^ocalculusandstochasticdierentialequationsthatyouarealreadyfamiliarwith.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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