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- quantitativ3
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Solution to Ito Process
Need some help/hints to finding the solution to the following Ito processs = sigmau = drift term, constantWt = brownian motiondYt = (u - Yt)dt + sdWt - 0.5s^2dtie what is Yt?
Solution to Ito Process
It is a standard Ornstein Uhlenbeck process with mean u-0.5s^2, volatility s and speed of mean reversion equal to 1.
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- KajetanSikorski
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Solution to Ito Process
Apply Ito's Lemma to Yt e^t and integrate
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- quantitativ3
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Solution to Ito Process
My original process is dXt = (u - logXt)Xt dt + sXt dWtI was told to apply transformationYt = logXt dYt = (u - Yt)dt + sdWt - 0.5s^2dtMy next step is to find Yt and from there find XtSo I'm not sure what you mean by Apply Ito's Lemma to Yt e^t and integrate
Last edited by quantitativ3 on February 18th, 2012, 11:00 pm, edited 1 time in total.
Solution to Ito Process
Since googling does not seem to be to your liking I'll make my hint a little more explicit: http://en.wikipedia.org/wiki/Ornstein%E ... ck_process
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- KajetanSikorski
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Solution to Ito Process
Why don't you at least try to do what I said before asking for more help? Or read the article as suggested by bearish.
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- quantitativ3
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Solution to Ito Process
sorry I was too engrossed with trying to integrate Yt and missed the obvious hints you guys dropped. It helped a lot to see the original equation and verify the solution to the SDE.Thank you for all the help.