Assume X is an It process. Use Its formula to derive the following: (a) Define Yt =

Assume X is an Itô process. Use Itô’s formula to derive the following:

(a) Define Yt = eXt . Show that dY Y = dX +

1 2

(dX)

2 .

(b) Assume X is strictly positive. Define Yt = logXt. Show that dY = dX X − 1 2

dX X

2

.

(c) Assume X is strictly positive. Define Yt = X−λ

t for a constant λ. Show that dY Y = −λ

dX X

+ λ(1+λ)

2

dX X

2

.