Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Use It's formula to verify that the following processes

Question:

Let $\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$. Use Itô's formula to verify that the following processes are martingales:

\[X_{t}=e^{t / 2} \cos B_{t} \quad \text { and } \quad Y_{t}=\left(B_{t}+tight) \exp \left(-B_{t}-t / 2ight) \text {. }\]

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

Step by Step Answer:

Related Book For answer-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

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...
XYZ What is the difference between volatile and nonvolatile memory? Is RAM volatile or nonvolatile? Is ROM volatile or nonvolatile? 7.9 Registers perform a very important role in the fetch-execute...
Super Slushie charges $6.50 for a medium slushie and $9 for a large slushie. Their total net marketing contribution is $28,000 per week. They want to raise the price of each slushie 12.5% next month...
Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United...
Food scientists have created a new oil. At room temperature, the oil is a liquid. As the oil gets colder however, it stiffens (thickens) into a sticky gel. To explore the properties of the oil, the...
Many researchers are interested in the transcription of protein-encoding genes in eukaryotes. Such researchers want to study mRNA. One method that is used to isolate mRNA is column chromatography....
MicroProducts, Incorporated (MPI) manufactures printed circuit boards for a major PC manufacturer. Before a board is sent to the customer, three key components must be tested. These components can be...
You are the Director of the 6 ICU units at your facility. You have an all RN staff and CNA's in each of the units. Your CNO has recently informed you that he has performed a supply audit and has...
Let $B_{t}=\left(b_{t}, \beta_{t}ight), t \geqslant 0$ be a $\mathrm{BM}^{2}$ and set $r_{t}:=\left|B_{t}ight|=\sqrt{b_{t}^{2}+\beta_{t}^{2}}$. a) Show that the stochastic integrals...
Prove Theorem 5.6 using It's formula. Data From Theorem 5.6 5.6 Theorem. Let (Bt, Ft)to be a d-dimensional Brownian motion and assume that the Ex. 5.10 function fee.2 ((0, co) x Rd, R) ne([0, o) x...
Footware, Inc., is a small manufacturer of shoes. The company has two divisions: the Sandal Division and the Moccasin Division. Data for the month of October are as follows: Junette, the company's...
Suppose that you decide to hold the bonds in the previous question for a year, and then sell them. The next year, the interest rate on comparable bonds increases to 9.5%. How much will you be able to...
1. What is the FV difference between an annuity that pays you $1000 each year for 5 years at the beginning of the period, versus an annuity that pays you $1000 each year for 5 years at the end of the...
You work at NBI Conveyancing. Your supervisor has asked you to put together a training program for law students who are arriving next week to start their summer internship. The presentation must...
6) You are a 50/50 partner in a BBQ restaurant. Your business partner, who majored in English Literature, wants to invest in a new, larger, more efficient smoker. Including delivery, the new smoker...
Discuss the effect of the following identified risk on: Risk of Material Misstatement, Detection Risk, and the overall audit effort: Apollo's sales manual requires that orders greater than $10,000...
The electric field in an EM wave travelling north oscillates in an east-west plane. Describe the direction of the magnetic field vector in this wave.
Show that if A is any m n matrix, then Im A = A and AIn = A.
Is it true that for an expected utility maximizer to be a risk averter, his/her utility function should have a negative second derivative? Let u(x) = x for x [0,1], and u(x) = 1/2 + 1/2x for x 1....
(a) Is Condition Z from Section 2.3 a requirement on (i) distribution functions, or (ii) random variables, or (iii) the preference order under consideration? (b) Is Condition Z based on the concept...
Take real data on the daily stock prices for the stocks of two companies for one year from, say, http://finance.yahoo.com or another similar site. Considering a particular utility function, for...
Question 1 Evaluate the sources of value creation and value capture in the medical instruments and supplies industry. In your answer, aim to address the following questions: a) How did Intuitive...
Cash 3000 Current liabilities 5000 Other current assets 7000 Long-term debt 25000 Non-current assets 50000 Equity 30000 Income statement Operating income 6000 Interest payment 2500 Income before...
4. How have the required reserves and excess reserves held changed since the Financial Crisis? Use the excess reserve (EXCSRESNS) and required reserve (REQRESNS) variables to construct a graph from...

Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Use It's formula to verify that the following processes

Question:

Step by Step Answer:

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

Students also viewed these Business questions