MAT 236A (Stochastic Dynamics) (Fall 2022)
Course Materials

A critique of "quants" in Financial Times and a response by Steven E. Shreve from Carnegie Mellon University.
Complete slides for much of the background material for this course are on my MAT 235B page.
For complete proofs of fundamental theorems of asset pricing in discrete setting, see Chapter 4 of the book "Risk-Neutral Valuation" by N. H. Bingham and R. Kiesel, Springer 2004.

Homework 1. Due Oct. 5.

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.

MATLAB files: Brownian motion; random walks.

Homework 2. Due Oct. 12.

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

Homework 3. Due Oct. 19.

Homework 4. Due Nov. 2.

MATLAB file: stochastic integral.

Homework 5. Due Nov. 9.

MATLAB files: time change; representation of exponent; representation of maximum.

Homework 6. Due. Nov. 23.

MATLAB files:
Girsanov transformation; Brownian motion hitting time of a tilted line with density function.
Convergence of Picard iterations with drift function and fluctuation function.
Numerical solution to SDE by Euler-Murayama method.
Black-Scholes simulation.

Final exam. Due Wed., Dec. 7, 4pm.