Homework Help is Here – Start Your Trial Now!
Math
Statistics
PROBLEM 2: Ito's Formula in Action Consider the SDE: dX = aX dt + b(t) X dW with X(0) = 1 Here a is a constant and b(t) is a function of t. Use Ito to show that X(T) is distributed lognormally for all future values of time T. Can you write VAR[log(X(T)] as a function of T? How about VAR[X(T)]?

PROBLEM 2: Ito's Formula in Action Consider the SDE: dX = aX dt + b(t) X dW with X(0) = 1 Here a is a constant and b(t) is a function of t. Use Ito to show that X(T) is distributed lognormally for all future values of time T. Can you write VAR[log(X(T)] as a function of T? How about VAR[X(T)]?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
4
PROBLEM 2: Ito's Formula in Action Consider the SDE: dX = ax dt + b(t) X dW with X(0) = 1 Here a is a constant and b(t) is a function of t. Use Ito to show that X(T) is distributed lognormally for all future values of time T. Can you write VAR[log(X(T)] as a function of T? How about VAR[X(T)]?
Transcribed Image Text:PROBLEM 2: Ito's Formula in Action Consider the SDE: dX = ax dt + b(t) X dW with X(0) = 1 Here a is a constant and b(t) is a function of t. Use Ito to show that X(T) is distributed lognormally for all future values of time T. Can you write VAR[log(X(T)] as a function of T? How about VAR[X(T)]?
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS