# Questions tagged [stochastic-calculus]

A branch of mathematics that operates on stochastic processes.

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### Clarification on Paul Wilmott's derivation of Ito's Lemma

I'm currently self-studying to be quant and have been thoroughly enjoying PW's book. I have some questions regarding his derivation of Ito's lemma. Specifically, I can see that the first line in his ...
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### Is it fair in an introductory stochastic calculus/derivatives pricing class to ask for the price when absence of arbitrage is violated? [closed]

Re close votes: I believe this is a fair kind of opinion-based question because it's like those ethics questions in academia se or workplace se or because it's pedagogical. Context: I'm actually ...
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### Compare errors in estimating a probability

Let $X_t$ be a geometric Brownian motion: $dX_t = \mu(X_t,t)dt + \sigma(X_t,t)dW_t$ with $W_t$ a standard Brownian motion. Given the intervals $[t_{j-1}, t_{j}]$ for $j\in {1,...,U,...,N}$, let $M_j$ ...
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### Is it a problem that there are so few stocks in the generalized Black Scholes market? [duplicate]

In the standard Black Scholes market there is only one stock. In the generealized market there can be a finite amount, but my impression is that there are few stocks in the market. The real world ...
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### Calculating futures price

Consider a world as follows: $$\frac{dB}{B} = r_tdt$$ $$\frac{dS}{S} = r_tdt - 0.05dW_1 + 0.5dW_2$$ $$dr_t = 0.2 dW_1$$ where $r_0=0$. The Wiener processes $W_1$ and $W_2$ are independent. The price ...
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I'm new to stochastic calculus and try to calculate (1) mean and (2) variance of $$\int_s^t W_u du$$ where $W_u$ is a Brownian motion. I already found this helpful answer, where it was shown that $\... 0answers 44 views ### Equivalence of two definitions of the stochastic integral The Question I am reading Shreve's Stochastic Calculus for Finance, Volume II. On page 145, definition (4.4.20), he defines an integral with respect to an Itô process. Definition 4.4.5. Let$X(t) = X(...
I'm reading Shreve's Stochastic Calculus for Finance, Volume II. In it, he uses the stochastic differential notation. For example, he may write \mathrm{d}X(t) = \sigma(t)\mathrm{d}W(t)+\alpha(t)\...
I'm working my way through an elementary stochastic calculus textbook. I'm having trouble with one of the questions: Bachelier type stock price dynamics. Let the SDE for stock price $S$ be given by \$...