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时间:2021-02-11
《金融工程数值方法分析5171923781.ppt》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、CHAPTER4elementarystochasticcalculusInthisChapterallthestochasticcalculusyouneedtoknow,andnomorethemeaningofMarkovandmartingaleBrownianmotionstochasticintegrationstochasticdifferentialequationsIto’slemmainoneandmoredimensionsStochasticcalculusisveryimportantinthemathematicalmodelingoffi
2、nancialprocesses.Thisisbecauseoftheassumedunderlyingrandomnatureoffinancialmarkets.ThedistributionofthevalueoftherandomvariableSiconditionaluponallofthepasteventsonlydependsonthepreviousvalueSi−1.ThisistheMarkovproperty.Wesaythattherandomwalkhasnomemorybeyondwhereitisnow.martingaleproper
3、ty:QUADRATICVARIATION(二次变分二次变差):definethequadraticvariationoftherandomwalkas:Example:tossingacoin.stochasticdifferentialequations:随机微分方程:Itˆo’slemma,SOMEPERTINENTEXAMPLES:ExampleNo.1:thesimpleBrownianmotionSOMEPERTINENTEXAMPLES:ExampleNo.2:TheLognormalRandomWalkSOMEPERTINENTEXAMPLES:Exa
4、mpleNo.3:AMean-revertingRandomWalk
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