Questions tagged [stochastic-integral]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
0answers
38 views

Distribution of Stochastic Integral Example

I am looking for help on justifying how the integral $$\int_{0}^{t} (t-s) \, dW_{s}$$ is normally distributed. I realize that the general fact that Ito Integrals with deterministic integrands are ...
2
votes
1answer
113 views

Why this stochastic integral is calculated with Riemann integral

This picture is from Neftci's textbook, 'An Introduction to the Mathematics of Financial Derivatives, Third Edition' What makes me uncomfortable is equation [10.61] In above picture. In this equation,$...
6
votes
1answer
216 views

Parametric Stochastic Integral

I need help. Defining the parametric stochastic integral $$ F_t = \int_t^T\xi(t,s)g(s)ds $$ $\\\\$ with $\xi$ a generic stochastic process such that $d\xi(t,s) = \mu(t,s)dt + \sigma(t,s)dW_t$, I'm ...
0
votes
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(...
1
vote
1answer
172 views

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 ...
1
vote
0answers
63 views

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 ...
1
vote
1answer
39 views

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 ...