MAT 236A (Stochastic Dynamics) (Fall 2012)
Course Materials

All files are in the pdf format, which require the free Adobe Acrobat reader.
A critique of "quants" in Financial Times and a response by Steven E. Shreve from Carnegie Mellon University.
For complete proofs of fundamental theorems of asset pricing, see Chapter 4 of the book "Risk-Neutral Valuation" by N. H. Bingham and R. Kiesel, Springer 2004.

Homework 1. Due Oct. 12. (LaTex file.)

P. Billingsley's 1974 paper on weak convergence of probability measures is still a good exposition on Brownian motion as a limit of random walks. Same author's book "Convergence of Probability Measures" (Wiley, 1999) is a classic on the topic.

Homework 2; scanned page from Baxter-Rennie book. Due Oct. 19. (LaTex file.)
Oct 15, 2pm: A typo in problem 3 fixed.
Oct 17, 3pm: Typo: The homework is actually due Fri., Oct 19.

"Brownian motion" by Peter Mörters and Yuval Peres (Cambridge, 2010) covers Brownian motion sample path properties. Go to Yuval Peres's web page for a pdf copy of this excellent book.

Homework 3. Due Oct. 26. (LaTex file.)

MATLAB files: Brownian motion; random walks; stochastic integral.

Homework 4. Due Nov. 9. (LaTex file.)

Homework 5. Due Nov. 16. (LaTex file.)

MATLAB files: Brownian motion maximum replication by stochastic integral; time change of a stochastic integral that makes it into a Brownian motion.

If interested, check out lecture notes on Malliavin calculus by Eulalia Nualart.

Homework 6. Due Nov. 26. (LaTex file.)

Homework 7. Due Dec. 10. (LaTex file.)
Nov. 29, 5pm: Ignore the first sentence in Problem 2, as it is repeated later in 2(b).
Dec. 3, 12:20pm: Problem 2(c) should read "... minimizes the expression in (b)."

MATLAB files: Brownian motion hitting time of a tilted line simulation and density; SDE solver with a sample drift and fluctuation functions; Black-Scholes simulation; and Kolmogorov forward equation solver with a sample drift and fluctuation functions.