Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a one-dimensional Brownian motion and (f in mathcal{C}^{1}(mathbb{R})). Show that (M_{t}:=f(t)
Question:
Let \(\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}\) be a one-dimensional Brownian motion and \(f \in \mathcal{C}^{1}(\mathbb{R})\). Show that \(M_{t}:=f(t) B_{t}-\int_{0}^{t} f^{\prime}(s) B_{s} d s\) is a martingale.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
We can prove that Mt is a martingale by showing it satisfies the properties of a martingale Heres ho...View the full answer
Answered By
Akshay Agarwal
I am a Post-Graduate with a specialization in Finance. I have been working in the Consulting industry for the past 8 years with a focus on the Corporate and Investment Banking domain. Additionally, I have been involved in supporting student across the globe in their academic assignments and always strive to provide high quality support in a timely manner. My notable achievements in the academic field includes serving more than 10,000 clients across geographies on various courses including Accountancy, Finance, Management among other subjects. I always strive to serve my clients in the best possible way ensuring high quality and well explained solutions, which ensures high grades for the students along-with ensuring complete understanding of the subject matter for them. Further, I also believe in making myself available to the students for any follow-ups and ensures complete support and cooperation throughout the project cycle. My passion in the academic field coupled with my educational qualification and industry experience has proved to be instrumental in my success and has helped me stand out of the rest. Looking forward to have a fruitful experience and a cordial working relationship.
5.00+
179+ Reviews
294+ Question Solved
Related Book For
Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook
ISBN: 9783110741254
3rd Edition
Authors: René L. Schilling, Björn Böttcher
Question Posted:
Students also viewed these Business questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
Miller-Rabin test to check whether a number N is composite. This will involve computing a N1 mod N for some value of a. [10 marks] Carry out the steps for N = 65 and a = 1, 2, 8 and 12. on what each...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Two positive charges, each with charge q = 2.5 nC, are placed as shown in the diagram. The distance d 0.42 m. Find the net electric potential at the point x = 0, y = 0.12 m.
-
What is no-fault insurance?
-
Team Project Useful Formulas for Two and more Vectors, prove (12) ?? (16), which are often useful in practical work, and illustrate each formula with tow examples. Show that each side of (13) then...
-
Jack DeCoster owned Quality Egg, LLC, an Iowa egg production company. Jacks son, Peter DeCoster, served as the companys chief operating officer. Jack also owned and operated several egg production...
-
The Edelman Gem Company, a small jewelry manufacturer, has been successful and has enjoyed a good growth trend. Now Edelman is planning to go public with an issue of common stock , and it faces the...
-
4. Ethan bought new car worth $60 000. After 5 years, the car was worth $35 429.40. Calculate the depreciation rate of the Ethan's car. [T4] [C2]
-
Let \(\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}\) be a \(\mathrm{BM}^{d}\). Show that \(X_{t}=\frac{1}{d}\left|B_{t}ight|^{2}-t, t \geqslant 0\), is a martingale.
-
Let \(\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}\) be a one-dimensional Brownian motion. Which of the following processes are martingales? a) \(U_{t}=e^{c B_{t}}, c \in \mathbb{R}\); b)...
-
A local politician has budgeted at most $80,000 for her media campaign. She plans to distribute these funds between TV ads and radio ads. Each one-minute TV ad is expected to be seen by 20,000...
-
A US motivational speaker was brought in by a South African private company as part of its annual general meeting to speak to the sales and marketing staff. Part of the presentation included...
-
1. Despite the higher cost, air freight will likely continue its upward growth. The increasing demand for perishables, chemicals and valuables are some of the key factors in this trend. Delays at...
-
On March 10, Barrett, Inc., declared a $17,000 account receivable from the Lamas Company as uncollectible and wrote off the account. On November 18, Barrett received an $11,000 payment on the account...
-
importance of having corporate governance as per the king 3/king 4 report. illustrate with examples. (30 marks) Critically discuss the barriers and challenges to managing diversity( 20 marks) draft a...
-
On January 1, Hemi Corporation issued $350,000 of 9-year, 8% bonds for $309,086 yielding an effective interest rate (yield to maturity) of 10%. Interest is paid-semi-annually on June 30 and December...
-
As nearly morning passed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to change the f -number from f /5.6 to f /22. By...
-
Use the graphs of f and g to graph h(x) = (f + g) (x). To print an enlarged copy of the graph, go to MathGraphs.com. 1. 2. y 24 8. 2. -2 -2 4 6
-
Using the convolution formula, show that the sum of two independent standard normal r.v.s is normal with mean 0 and variance 2 (which is consistent with Proposition 5). (Advice: First, show that...
-
Let X and Y be independent continuous random variables with the densities e (x1)2 and respectively. Using Table 3 from the Appendix, estimate P(2 S 4), where S = X +Y.
-
A signal, when going through an electronic device, is distorted, which amounts to adding a random distortion error X. Suppose that X is normal with zero mean and a standard deviation of . The latter...
-
1. There is an interesting optical effect you have likely noticed while driving along a flat stretch of road on a sunny day. A small, distant dip in the road appears to be filled with water. You may...
-
A helicopter with mass 2.85 x 104 kg has a position given by (t) = (0.020) + (2.2t) - (0.060t) m. Find the net force on the helicopter at t = 3.1 s. Fnet 'net = 2+ 3+ k kN
-
1. [15 marks total] Consider a mass of air in the atmosphere (a "cold front"), consisting of a rectangular prism 100. km x 100. km at its base and 1.00 km high (see the sketch below, which is not to...
Study smarter with the SolutionInn App