Math 599 Fall 2004 Syllabus

Math 599, Introduction to Forward-Backward Stochastic Differential Equations, Fall 2004

Time and location: MW 4:45-6:00pm, DRB 337
Office hours: MWF 2:00-3:00pm, DRB 354

Text: Forward-Backward Stochastic Differential Equations and Their Applications, Lecture notes in Mathematics, 1702, Springer, (1st ed. 1999. Corr. 2nd printing, 2000), by Jin Ma and Jiongmin Yong

Instructor: Jianfeng Zhang
Office: DRB 354, (213)740-9805
Email: jianfenz@usc.edu
Homepage: http://math.usc.edu/~jianfenz
Presentation schedule and papers

Course Description: In this course we will introduce the basic theory of Backward SDEs and Forward-backward SDEs, and their connections with PDEs, stochastic control and mathematical finance.

Topics Covered: Review of SDE theory, well-posedness of BSDEs, nonlinear Feynman-Kac formula, four-step scheme, FBSDE and option pricing theory, FBSDE and HJB Equation. Some further properties of the martingale integrand (the Z part) of the solution to BSDEs may also be discussed, if time allows.

Homework: The techniques used in the course are as well important. The homework assignments will provide students good opportunities for practice, and thus will be a very important part of the course. Students are (strongly) encouraged to discuss the problems together, but each one should write down the solutions independently.

Presentation: During the last week of classes, students (maybe in groups) will be asked to give a presentation about a topic related to the subject matter of the course. The students may choose the paper, but should get approved by the instructor before October 31.

Final Exam: A take-home final exam will be handed out around Thanksgiving, and due in the end of the semester. Students are not permitted to discuss the problems with others.

Prerequisite: Math 509 (or equivalent courses on SDEs)

Grading Policies: 10% on class participation, 40% on homework, 40% on final take-home exam, and 10% on final presentation.

The final exam will be graded by the instructor. The homeworks will be collected about every two weeks, but will only be checked for completeness. Students are welcome to discuss homework problems with the instructor, and solutions to some selective problems may be given (upon students' request).

Feedback and Questions: It is very useful to get feedback and questions, both inside and outside class. You are very welcome to visit me during my office hours. You can also make appointments to see me at other time.