# Questions tagged [stochastic-integrals]

This tag is used for questions about stochastic integrals – especially for calculations. For questions related to more theoretical aspects of stochastic integrals such as their constructions, (stochastic-analysis) may be more appropriate.

1,303 questions
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### Proving one form of Ito Isometry using Functional Analysis

I would like to know whether it is possible to give a proof of (one form of) Ito Isometry using a tool which I like to call "the functional analysis"-way. Let me explain the settings first. What we ...
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### Black-Scholes model with time-dependent volatility

We consider the Black-Scholes model with time-dependent volatility $\sigma(t)$: $$dS_{1}(t)=rS_{1}(t)dt+\sigma(t)S_{1}(t)dW(t)$$ The question: what constant $\hat{\sigma}$ one needs to apply such ...
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### Solution of a second order Stochastic Differential Equation

Consider the following SDE $$dx = (-ax)dt + \sigma db\\ dy = (-by+e^{-x})dt$$ where $a,b,\sigma>0$ and $b$ is a browninan motion PROBLEM: What is the solution of this system? How can I estimate ...
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### How to compute ito's calculus without knowing its solution already?

I'm having trouble computing Itô's calculus. Take $\int_0^tB_sdB_s$ for example, can I solve it base solely on Itô-Doeblin Formula, instead of assuming $f(x)=\frac{x^2}{2}$? Please help!