# Questions tagged [itos-lemma]

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### Multivariate Itô's lemma

Hey guys I'm looking for worked examples who show how to apply Itô's lemma in several variables, starting from the very basics. Thank you in advance!
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### Dixit & Pindyck (1993) Chapter 4, equation 13

Starting with the Bellman equation for the optimal stopping problem: $$F(x,t)=max\{\Omega(x,t), \pi(x,t)+(1+\rho dt)^{-1} E[F(x+dx, t+dt)|x]\}$$ In the continuation region where the second term is the ...
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### How to proof the formula to be martingale under ITO process?

How can implies that is a martingale when using the defaultable bond price?
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### Confirm If Risk-Neutral Measure is Unique in My Following Case

I'm reading a book that discusses about derivatives pricing and have some doubts about a particular problem and really appreciate your advice: Question: Assume a non-dividend paying stock follows a ...
Let $S_t$ be a geometric brownian motion and let $M_t = \sup_{0 \le u \le t} S_t$ be the maximum process. Define $X_t = \frac{M_t}{S_t}$. A book I am reading states the following: How does this ...
I am trying to derive the differential of the product of two processes, but I got stuck. This is what I have until now: We have the following two stochastic processes: $dX_t= \mu_t dt +\sigma_t dW_t$...