# Questions tagged [stochastic-calculus]

A branch of mathematics that operates on stochastic processes.

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### Process with negative quadratic variation

Today seems to be question day for me, sorry. The complex process $$dX = i\sigma dW$$ where $i = \sqrt{-1}$ and $dW$ is a standard (real-valued) Brownian motion will have a negative variance ...
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### Steven Shreve: Stochastic Calculus and Finance

The lecture notes have the following theorem: Let $\theta\in \mathbb{R}$ be given and $B(t)$ stands for the Brownian motion which is a martingale, then $Z(t)=exp\{-\theta B(t)-\dfrac{1}{2}\theta^2t\}$...
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### What is the SDE of this equation? [closed]

I am new and struggling to understand how to solve this using Ito lemma. Can someone please explain it to me: $$dS_t=-\frac{1}{2}\sigma^2 S_t dW_t$$ what is the solution with explanation please
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### Covariance of logarithms of geometric Brownian motion

Suppose I have a Geometric Brownian Motion process, $$dX_t=\mu X_t dt + \sigma X_t dW_t$$ I'd like to find the covariance of $\log(X_t)$ and $\log(X_s)$ where $s<t$. We can write $\log(X_t)$ in ...
41 views

### What is Variance of delta of brownian motion [closed]

I am new to this. If variance of Brownian motion b is t, what is the variance of db? db is delta of b