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Introduction to Ito's Lemma

Introduction to Ito s LemmaWenyu ZhangCornell UniversityDepartment of Statistical SciencesMay 6, 2015 Wenyu Zhang (Cornell)Ito s LemmaMay 6, 20151 / 21 Overview1 Background2 Ito Processes3 Ito s LemmaWenyu Zhang (Cornell)Ito s LemmaMay 6, 20152 / 21 BackgroundProved by Kiyoshi Ito(not Ito s theorem on group theory by NoboruIto)Used in Ito s calculus , which extends the methods of calculus tostochastic processesApplications in mathematical finance derivation of theBlack-Scholes equation for option valuesWenyu Zhang (Cornell)Ito s LemmaMay 6, 20153 / 21 Ito ProcessesQuestionWant to model the dynamics of processX(t) driven by Brownian motionW(t).

Brownian Motion - An Introduction to Stochastic Processes (2012) CUHK course notes (2013) Chapter 6: Ito’s Stochastic Calculus Karl Sigman Columbia course notes (2007) Introduction to Stochastic Integration Wenyu Zhang (Cornell) Ito’s Lemma May 6, 2015 21 / 21

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  Introduction, Calculus, Stochastic, Stochastic calculus, Introduction to stochastic

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