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Ito's Lemma

  1. Dec 12, 2009 #1
    Does anyone know a document that explains the construction of Ito's lemma? In most financial mathematics textbooks, it's poorly motivated.

    Thanks!
     
  2. jcsd
  3. Dec 13, 2009 #2

    HallsofIvy

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    Try this:
    http://www.contingencyanalysis.com/archive/archive99-4/00000264.htm [Broken]
     
    Last edited by a moderator: May 4, 2017
  4. Dec 13, 2009 #3
    Wow nice, is there more?
     
  5. Dec 14, 2009 #4
    Actually nevermind about that, what about the stochastic perturbation of the chain rule?
     
  6. Dec 15, 2009 #5
    I'm taking an undergrad course on stochastic processes right now, and all of our course materials are online. They aren't necessarily the best, in my opinion, but you may find them useful. If his notes themselves aren't useful to you, he usually includes very specific references so you can find the info elsewhere.

    I'm pretty sure he doesn't give the most general version of Ito's Lemma/Formula here, but since you mentioned mathematical finance in your post, I think it'll probably be good enough. Anyway, here it is:

    http://www.math.unl.edu/~sdunbar1/MathematicalFinance/Lessons/StochasticCalculus/ItosFormula/itosformula.xml [Broken]

    In case you're interested, here's a page with all of the materials from the course: http://www.math.unl.edu/~sdunbar1/MathematicalFinance/mathfinance.shtml

    Hope that helps!
     
    Last edited by a moderator: May 4, 2017
  7. Dec 15, 2009 #6
    I just want to know the motivation behind the stochastic perturbation of the chain rule.

    Ask your prof and see if he knows, lol
     
  8. Dec 15, 2009 #7
    If I understand what you are asking, the link I posted explains it. Read "Example 1" where he shows how using the ordinary chain rule fails. He goes on to show that Ito figured out that he could use an algebraic identity and the quadratic variation of Brownian Motion to derive a new chain rule that accounts for the stochasticity.
     
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