Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (X_{t}=exp left(a B_{t}+b tight), t geqslant 0),

Question:

Let $\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$. Show that $X_{t}=\exp \left(a B_{t}+b tight), t \geqslant 0$, is a martingale if, and only if, $a^{2} / 2+b=0$.

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

Step by Step Answer:

Related Book For book-img-for-question

Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

ISBN: 9783110741254

3rd Edition

Authors: René L. Schilling, Björn Böttcher

See More Books

Question Posted: Mar 17, 2024 01:00 AM

See More Questions

A system is described by x = Ax + Bu where and x1(0) = x2(0) = 10. Determine x1(t) and x2(t). 0 2 2
Find a least-squares solution of Ax = b by (a) Constructing the normal equations for x (b) Solving for x. A = 1-2 2 3 5 -1 0 2 b || 1 -4 2
Waystar Corporation went public last year. The IPO offered 4,000,000 shares for sale at $2.30 per share and was fully subscribed. On the first day of trading the stock price rose to $7.11. How much...
Racing Investment Fund 2000 LLC was created in August 2000 to purchase, train, and race thoroughbred horses. The LLC ' s operating agreement provided for 50 membership units to be sold for an initial...
What is the TDS ratio?
When using the effective-interest method of amortization, the book value of the bonds changes by what amount on each interest payment date? a. interest expense c. amortization b. cash interest...
What is wrong with using the cost of the specific capital used to finance a project as the discount rate in relation to that project?
Consider the composite solid shown. Solid A is a thermally conductive material that is 0.5-cm thick and has a thermal conductivity, k A = 50 W/m K. The back side of solid A (x = 0) is thermally...
Exercise 12-5 Volume Trade-Off Decisions [LO12-5] Outdoor Luggage, Inc., makes high-end hard-sided luggage for sports equipment. Data concerning three of the company's most popular models appear...
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)...
Let $p(t, x)=(2 \pi t)^{-d / 2} \exp \left(-|x|^{2} /(2 t)ight), x \in \mathbb{R}^{d}, t>0$, be the transition density of a $d$-dimensional Brownian motion. a) Show that $p(t, x)$ is a solution...
How could we use the margin of safety to calculate the percent change in profit given a percent change in sales?
Zephyr Minerals completed the following transactions involving machinery. Machine No. 1550 was purchased for cash on April 1, 2020, at an installed cost of $75,000. Its useful life was estimated to...
Kelly is a self-employed tax attorney whose practice primarily involves tax planning. During the year, she attended a three-day seminar regarding new changes to the tax law. She incurred the...
At a recently concluded Annual General Meeting (AGM) of a company, one of the shareholders remarked; historical financial statements are essential in corporate reporting, particularly for compliance...
4. In hypothesis, Mr. Ng wants to compare the solution in Q3 to other solutions in different conditions. If the following constraints are newly set in place, answer how much different is going to be...
3C2H6O2+7H2O= C2H4O3+11H2+O2+H2C2O4+CH2O2 Glycolic acid is produced electrochemically from ethylene glycol under alkaline conditions(NaOH). Hydrogen is produced at the cathode, and formic acid and...
Give an example of a three variable study for which a mediation analysis would make sense. Be sure to make it clear which variable is the proposed initial predictor, mediator, and outcome.
Starr Co. had sales revenue of $540,000 in 2014. Other items recorded during the year were: Cost of goods sold ..................................................... $330,000 Salaries and wages...
Let us revisit the record value problem of Section 3.2.3. Make sure that all reasonings there remain true in the case where Xs are continuous. Show that in this case and that P(N for n = 1,2, ......
A random vector (X,Y) has the joint density function Find c. Guess whether X and Y are independent. Justify your answer. Write the marginal densities.
Suppose that a r.vec. X = (X 1 ,X 2 ) has the distribution uniform on the circle (not a disk!) x 2 1 +x 2 1 = r 2 for a fixed r. This means that the vector X takes values (x 1 ,x 2 ) only from the...
question 1- You borrow a simple loan of SR 500,000, interest rate is 20%, it matures in one year. what's the yied to maturity? question 2- calculate_i for One-Year Discount Bond with price(p) =...
Taste of Muscat is a reputed chain of restaurants operating in Oman. Assume You are working as a management accountant for this restaurant chain which is specialized in all types of Arabic food. Your...
Industry Current Year Minus 1 Current Year Minus 2 Company: Air Products and Chemicals, Inc. (APD) Stock Price: 306.72 USD Shares Outstanding: 220.89 M Financial Ratios Most Current Year Current...

Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (X_{t}=exp left(a B_{t}+b tight), t geqslant 0),

Question:

Step by Step Answer:

Martingale Property A proces...View the full answer

Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

Students also viewed these Business questions