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)]?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 70E

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Question

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)]?

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