Questions tagged [stochastic-integral]

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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(...
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What does it mean to “compute” an Itô integral?

I'm reading Shreve's Stochastic Calculus for Finance II. On page 191, Exercise 4.6, we are given the problem Exercise 4.6. Let $S(t)=S(0)\exp\Big \{\sigma W(t)+(\alpha-\frac{1}{2}\sigma^2)t\Big\}$ be ...
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How to solve/evaluate an Ito Integral?

I'm given the following Ito integral which I need to evaluate. $Z_t$ is the Brownian motion. My problem is that online resources aren't making much sense because of the notation, so it ends up leaving ...
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Regression of stochastic integral on Wiener process

This question is a follow-up from the following: conditional expectation of stochastic integral so I won't repeat myself regarding assumptions and notation. Using Brownian bridge approach, we know ...