Prove that, if (W) is a Brownian motion, from the definition of the stochastic integral as an

Question:

Prove that, if $W$ is a Brownian motion, from the definition of the stochastic integral as an $L^{2}$ limit, $\int_{0}^{t} W_{s} d W_{s}=\frac{1}{2}\left(W_{t}^{2}-t\right)$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Mathematical Methods For Financial Markets

ISBN: 9781447125242

1st Edition

Authors: Monique Jeanblanc, Marc Yor, Marc Chesney

See More Books

Question Posted: Apr 02, 2024 06:00 AM

See More Questions

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...
Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...
Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...
What (if anything) is wrong with each of the following statements? a. if (a > b) then c = 0; b. if a > b { c = 0; } c. if (a > b) c = 0; d. if (a > b) c = 0 else b = 0;
Singh Distributing Company, which uses the periodic inventory system, engaged in the following transactions during May of the current year: May 3 Purchased office supplies for cash, $22,000. 7...
Abhinav is a trader. Using the following information taken from Abhinavs books on 30 June 208: a. Prepare a trial balance at 30 June 208 b. Prepare an income statement for the year ended 30 June 208...
What is assignable variation? LO.1
On January 1, Intergen, Inc., invests $200,000 for a 40 percent interest in Ryan, a new joint venture with two other partners each investing $150,000 for 30 percent interests. Intergen plans to sell...
a) What is the relationship between PV and FV and how are they calculated? (10 Marks) b) You want to purchase a new TV and you are willing to pay $2,000. If you can invest at 10% per year and you...
If two martingales are independent, they are orthogonal. Check that the converse does not hold. Let $B$ and $W$ be two independent Brownian motions. The martingales $W$ and $M$ where...
Let $b$ and $\theta$ be continuous deterministic functions. Prove that the process $Y_{t}=\int_{0}^{t} b(u) d u+\int_{0}^{t} \theta(u) d W_{u}$ is a Gaussian process, with mean...
Consider the control system of Problem 9.2-2. Problem 9.2-2 Consider the plant of Problem 9.2-1, which has the transfer function, from Example 9.5, Problem 9.2-1 The plant of Example 9.1 has the...
How do you manage global and international teams? What would you do different?
Your friend is super excited about the results of their study! They examined whether different parenting styles [A] resulted in differences in anxiety levels among children. The different levels (a)...
Test the series for convergence or divergence. n=1 e1/n 78 O convergent O divergent
How do employees perceive the organization's vision and mission, and to what extent do these perceptions influence their commitment to the organization ?
In the table below which shows class taken and grade achieved, find the probability that a student selected takes Stat or receives a B grade. Round your answer to three decimal places 40 70 70 50 40...
Why is the quality school of management thought so popular?
For the data in Exercise 17-19, use the FIFO method to summarize total costs to account for, and assign these costs to units completed and transferred out, and to units in ending work in process....
Berbice Inc. has a new project, and you were recruitment to perform their sensitivity analysis based on the estimates of done by their engineering department (there are no taxes): Pessimistic Most...
#3) Seven years ago, Crane Corporation issued 20-year bonds that had a $1,000 face value, paid interest annually, and had a coupon rate of 8 percent. If the market rate of interest is 4.0 percent...
I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 100%. The volatility of my portfolio is A. 4% B. 14.4%...

Prove that, if (W) is a Brownian motion, from the definition of the stochastic integral as an

Question:

Step by Step Answer:

Mathematical Methods For Financial Markets

Students also viewed these Business questions