Prove that, for any (lambda in mathbb{C},left(e^{-lambda^{2} t / 2} cosh left(lambda W_{t} ight), t geq 0

Question:

Prove that, for any $\lambda \in \mathbb{C},\left(e^{-\lambda^{2} t / 2} \cosh \left(\lambda W_{t}\right), t \geq 0\right)$ is a martingale.

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

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...
"internet radios" for streaming audio, and personal video recorders and players. Describe design and evaluation processes that could be used by a start-up company to improve the usability of such...
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...
What would a profile look like across a restraining bend? Releasing bend?
Bubble Tea's accounts at December 31, 2017, included these unadjusted balances: Inventory......................................................... $ 4,400 Cost of Goods Sold...
Select the best answer. 1. A government opts to set aside $ 10 million of general-fund resources to nance a new city hall. Construction is expected to begin in several years, when the city has been...
Review the Ethical Focus feature, Whats in a Name? Youre Hired... or Not!, and use Bruners model of the perceptual process to explain why job applicants with ethnic-sounding names are less likely to...
1. Identify the stakeholders in this case. Identify their interests and Uniteds obligations to satisfy those interests from an ethical perspective. 2. Describe the ethical responsibilities of Tony...
How can you justify that unemployment may occur if the country raises its interest rates? Explain.
Let $W$ be a BM and $\varphi$ be an adapted process. (a) Prove that $\int_{0}^{t} \varphi_{s} d W_{s}$ is a BM if and only if $\left|\varphi_{s} ight|=1$, ds a.s. (b) Assume now that...
Prove that (v) of Definition 1.4.1.1 characterizes a BM, i.e., if the process $\left(Z_{t}=\exp \left(i \lambda X_{t}+\frac{\lambda^{2}}{2} t ight), t \geq 0 ight)$ is a $\mathbf{F}^{X}$-local...
What are some of the tasks suggested in technical support?
Campcraft is a small manufacturer of camping trailers. The business manufactures only one model and sells the units for $\$ 2500$ each. The variable costs of manufacturing and selling each trailer...
Describe W. Edwards Demings PDCA model.
Describe three reasons individuals resist change and indicate what should be done to correct them.
Describe Kurt Lewins three-step change model.
List and describe the three most common types of organizational structure.
Air is expanded from 400 kPa, 600 K in a polytropic process to 150 kPa, 400 K in a piston cylinder arrangement. Find the polytropic exponent n and the work and heat transfer per kg air using constant...
Presented below are income statements prepared on a LIFO and FIFO basis for Kenseth Company, which started operations on January 1, 2024. The company presently uses the LIFO method of pricing its...
As I am sure you know Bob Barker was the famous game show hostof the Price is Right. He was known for this slick white hair, hislove of animals, and his affection towards "Barker's Beauties".Bob's...
Answer all the below Questions A B F H G SMC E K L M N R 20 V W x Y 0 S T U Z 4 Externality a) In the above figure, there is (positive/negative). b) What is the free market equilibrium quantity? c)...
How can an information security audit be used to improve the security posture of an organization?

Prove that, for any (lambda in mathbb{C},left(e^{-lambda^{2} t / 2} cosh left(lambda W_{t} ight), t geq 0

Question:

Step by Step Answer:

To prove that leftelambda2 t 2 cosh leftlambda Wt ight t geq 0 ight is a martingale we need to show ...View the full answer

Mathematical Methods For Financial Markets

Students also viewed these Business questions