some solutions to øksendal’s stochastic differential equations + my ‘talk’ on the black-scholes formula

This spring, I did the Directed Reading Program (DRP) with the Math department; undergrads get paired with a PhD student to read a math book together. Columbia pays for the book. :)

Richard and I read the book on the right. (Thank you Richard for bearing with me!!)
We also worked through a few exercises, and I typed them up this week along with some notes to understand stuff a bit better. Since Øksendal’s own solutions are quite sparse, I wanted to post them here:

• Chapter 2: Some Mathematical Preliminaries - Probability Spaces, Random Variables, and Stochastic Processes

• Chapter 3: The Itô Integral

• Chapter 4: The Itô Formula and the Martingale Representation Theorem

• Chapter 5: Stochastic Differential Equations

• Chapter 7: Diffusions - Basic Properties

• Chapter 10: Application to Optimal Stopping

• Chapter 12: Application to Mathematical Finance

Also, I prepared a brief talk about the Black-Scholes formula derived in Chapter 12: