Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 236B: Stochastic Dynamics and Applications
Approved: 2009-03-01, Alfred Fannjiang
Units/Lecture:
Offered irregularly; 4 units; lecture/term paper or discussion
Suggested Textbook: (actual textbook varies by instructor; check your
instructor)
Prerequisites:
MAT 236A, or consent of instructor.
Course Description:
Stochastic processes, Brownian motion, Stochastic integration, martingales, stochastic differential equations. Diffusions, connections with partial differential equations, mathematical finance.
Suggested Schedule:
Department Syllabus
MAT 236B: Stochastic Dynamics and Applications
| Lectures | Sections | Topics/Comments |
|---|---|---|
| 3 | Chapters 2 - 3 | Review: Information/conditioning, Brownian motion, first passage time |
| 2 | 4.5 | Black-Scholes-Merton equation |
| 2 | 5.1 - 5.2 | Arbitrage theorem, risk-neutral measure, Black-Scholes-Merton formula |
| 3 | 5.3 - 5.4 | Fundamental theorems in asset pricing |
| 1 | 5.5 | Dividend paying stocks |
| 1 | 5.6 | Forwards and futures |
| 3 | Chapter 7 | Exotic options: barrier options, lookback options, Asian options |
| 3 | Chapter 8 | American derivatives |
| 3 | Chapter 9 | Change of numeraire: foreign and domestic risk-neutral measure, forward measure |
| 3 | Chapter 10 | Term-structure models |
| 5 | Chapter 11 | Rare events in finance, jump-diffusion processes |
Additional Notes:
COMMENT: This book focuses on the financial application of stochastic calculus. I have taught similar topics from other sources in 2006-2007 but did not find an ideal textbook that would give clear, in-depth coverage on both stochastic and finance. I hope Shreve's book will fit the bill (I am teaching from it this year, 2008-2009). For physical applications, the book Handbook of Stochastic Methods by Gardiner, comes to mind. It covers many interesting topics in physics and its best part is on the analysis/application of Fokker-Planck and master equations (rather than the stochastic calculus).