Questions tagged [stochastic-calculus]

A branch of mathematics that operates on stochastic processes.

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Evaluting the SDE $dX = tds$

The process $S$ is a geometric Brownian motion with an SDE: $dS = S(\sigma dB + \mu dt)$. I'm stuck evaluating $\int dX = \int tdS$, $E(X)$ and $V(X)$.
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integration of squared brownian motion w.r.t time

How to prove $\int_0^1 B_s^2ds$ is a random variable and compute its first two moments? From excercise 1.15 on the book martingales and brownian motion.
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Change of numeraire/probability when asset pays dividends

So I was looking at Margrabe's formula for exchange call options in the book 'Mathematical Methods for Financial Markets' (Jeanblanc, Chesney, Yor), and I was having trouble justifying their change of ...
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Integrating Brownian Motion [closed]

I just wonder how to integrate standard Brownian motion on time interval $(t, T)$. Let $Z$ be a standard Brownian motion with mean $0$ and standard deviation $1$, with $dZ^2 = dt$. How to derive the ...
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Bond Option Hedging

(My question) Please show me how to solve from (2) to (4) with computation processes. These are too difficult to solve. Thank you for your help in advance. (Cross-link) I have posted the same ...
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