Questions tagged [ito-calculus]

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Finding the distribution of $f(X_t)e^{-t}$ where $X_t$ is a stochastic process

Let $X_t$ be a continuous stochastic process with support on $[0,1$], and $f$ be a a.e. non-negative function on $[0,1]$. $X_t$ will be a solution to an SDE driven by Brownian motion I would like to ...
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Why are SDEs wrt different variables?

I am reading mathematical finance on my own. I am wondering how are differentiation wrt different variables defined. In stochastic calculus, we can see equations like, $dX_{t} = \mu dt + \sigma dW_{t}$...
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Solve Ito integral for continuous contributions to stock portfolio

I'm following Milevsky & Posner (2003) to model the value of a portfolio, $P$, assuming GBM (2) and a continuous contribution rate of $1$ (i.e. dollar-cost averaging): $$ \mathrm d S_t/S_t = \mu \...
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Solving Stochastic Integral with Ito's lemma

I want to solve the following: $\int\limits_{0}^{T} \exp[S(t)-t/2] \mathrm dW(t)$ where $\mathrm dS=µS \mathrm dt+\sigma S \mathrm dW$ is the Brownian motion. The Ito's formula I need to use reads: $\...