Find the explicit solutions of the following stochastic differential equations: (a) Ornstein-Uhlenbeck process: [d X_{t}=mu X_{t} d

Question:

Find the explicit solutions of the following stochastic differential equations:

(a) Ornstein-Uhlenbeck process:

\[d X_{t}=\mu X_{t} d t+\sigma d B_{t}\]

(b) Mean reverting Ornstein-Uhlenbeck process:

\[d X_{t}=\alpha\left(m-X_{t}\right) d t+\sigma d B_{t}\]

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

Step by Step Answer:

Related Book For book-img-for-question

Quantitative Finance

ISBN: 9781118629956

1st Edition

Authors: Maria Cristina Mariani, Ionut Florescu

See More Books

Question Posted: Apr 20, 2024 01:00 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...
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...
Let X space tilde thin space U left parenthesis 0 comma 20 right parenthesis and assume we take a sample of size 100 from this population distribution. What distribution would the sample mean (top...
Solve the Given Requirements by using this Equation: Tangent Lines and Derivatives. x + cos y = 1 a) Find dy b) Evaluate at dx c) Draw the tangent line at 35 1 y = 0 -1 -2 05 1.5 d) Write the...
Midwest Industries produces and distributes industrial chemicals in its Belco Division, which is located in Michigan's Upper Peninsula. Belco's earnings increased sharply in 2016, and bonuses were...
Explain how to measure and forecast market demand.
Im like the quarterback of the team. I manage 250 accounts, and anything from billing issues, to service issues, to selling the products. Im really the face to the customer, says Alison Capossela, a...
Do some reading in periodicals and/or on the Internet to find out more about the Sarbanes-Oxley Acts provisions for companies. Select one of those provisions, and indicate why you think financial...
Dividends Per Share Oceanic Company has 25,000 shares of cumulative preferred 3% stock, $150 par and 50,000 shares of $20 par common stock. The following amounts were distributed as dividends: Year 1...
Explain why your university is considered a system. Give examples of other systems that you know.
Use It's lemma to express $d F$ given that $F(x)=x^{1 / 2}$, where the stochastic process $\left\{S_{t}, t \geq 0 ight\}$ satisfies the stochastic differential equation \[d...
A system is dynamically coupled if the mass matrix for the system is not symmetric. Indicate whether the statement presented is true or false. If true, state why. If false, rewrite the statement to...
The combined weight of the load and the platform is 200 lb, with the center of gravity located at G. If a couple moment of M = 900 lb ft is applied to link AB, determine the angular velocity of links...
Due In: 06:48:23 Questions Question 1 (4) O Question 2 (8) Question 2 of 2 A company sold $150,000 bonds and set up a sinking fund that was earning 8.5% compounded semi-annually to retire the bonds...
Find the point on the graph of f(x) = x which is closest to the point (6, 27). How close is the closest point?
Due to a crash at a railroad crossing, an overpass is to be constructed on an existing level highway. the existing highway has a design speed of 50 mi/h. The overpass structure is to be level,...
Finding Bone Density Scores. In Exercises 37-40 assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard...
Interested in comparing the effectiveness of four different driving strategies, a government agency has equipped a compact car with a fuel- consumption meter that measures every 0.01 gallon of...
Prove that the mean heat capacities C P H and C P S are inherently positive, whether T > T 0 or T < T 0 . Explain why they are well defined for T = T 0 .
Docs Auto Body has budgeted the costs of the following repair time and parts activities for 2009: Doc's budgets 6,000 hours of repair time in 2009. A profit margin of $7 per labour hour will be added...
QUESTION 28 In a perpetual inventory system, the cost of inventory sold is: Debited to accounts receivable. Debited to cost of goods sold. O Not recorded at the time goods are sold. O Credited to...
The following financial statements and additional information are reported. IKIBAN INC. Comparative Balance Sheets June 30, 2019 and 2018 2019 2018 $105,709 69,500 66,800 4,700 246,700 127,eee...

Find the explicit solutions of the following stochastic differential equations: (a) Ornstein-Uhlenbeck process: [d X_{t}=mu X_{t} d

Question:

Step by Step Answer:

a OrnsteinUhlenbeck Process The stochastic differential equation SDE for the OrnsteinUhlenbeck process is given by dXt mu Xt dt sigma dBt To find the ...View the full answer

Quantitative Finance

Students also viewed these Business questions