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# Questions tagged [itos-lemma]

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### In what kind of stochastic process Ito's lemma is adopted?

I have been told that Ito's lemma serves as the stochastic calculus counterpart of the chain rule. And yet again my tutor mentioned it is not used for all stochastic processes. Is this statement true?...
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The Black Scholes model assumes the following dynamics for the underlying, well known as the Geometric Brownian Motion: $$dS_t=S_t(\mu dt+\sigma dW_t)$$ Then the solution is given: $$S_t=S_0\,e^{\... 2answers 2k views ### Why Ito calculus? Coming from physics, I am used to the fact that the Ito interpretation of most natural stochastic equations is wrong, and one should be using Stratonovich calculus instead (of course they are ... 1answer 394 views ### How to derive equivalent martingale measure using Ito's Lemma Can someone explain how to get equation 27.14 below? I understand the first usage of Ito's Lemma to get d(\ln f-\ln g) but I do not understand how to use Ito's Lemma to go from d(\ln \frac{f}{g}) ... 1answer 227 views ### Integration of stochastic total derivative Super basic question. I think I am doing this correctly, but just want a sanity check. Say I have a stochastic process r(t). Say I have an equation$$d(e^{\beta (t-s)}r(s))=\dots$$where the ... 1answer 413 views ### Ito's Lemma - Integrand depends on upper limit of integration A problem I came across while practicing using Ito's Lemma had a process with an integral whose integrand depends on the upper limit of integration (the goal is to find dZ_{t}): Z_{t}=\int_{0}^{t}... 5answers 2k views ### Monte carlo methods for vanilla european options and Ito's lemma. I understand that by applying Ito's lemma to the following SDE$$dX=\mu\,X\,dt+\sigma\,X\,dW$$one obtains a solution to the above SDE which is as follows:$${X}\left( t\right) =\mathrm{X}\left( 0\...
From the text book Quantitative Finance for Physicists: An Introduction (Academic Press Advanced Finance) I have this excercise: Prove that  \int_{t_1}^{t_2}W(s)^ndW(s)=\frac{1}{n+1}[W(t_2)^{n+1}-...