Math 509, Stochastic Differential Equations, Fall 2007

Time and location: MWF 1:00pm - 1:50pm, KAP 141.
Text: Stochastic Differential Equations: An Introduction with Applications, Fifth Edition, by Bernt Oksendal. Published by Springer (Universitext Series).
Instructor: Jianfeng Zhang, DRB 228, (213)7409805
Email: jianfenz@usc.edu Homepage: http://almaak.usc.edu/~jianfenz
Office hours: MW: 2:00pm-3:30pm, DRB 228

Course Content:
Brownian motion, stochastic integration, Ito's formula, martingale representation theorem, existence and uniqueness theorems for stochastic differential equations, diffusion processes, Feynman-Kac formula, Girsanov transformation. This corresponds more or less to chapters 2-5, 7 and 8 of the textbook.

The rest of the course will deal with some applications. Possible topics include filtering theory (Chapter 6), connections with elliptic linear partial differential equations (chapter 9), optimal stopping (Chapter 10), stochastic control (Chapter 11), and option pricing theory(chapter 12). The particular choice of material will depend on the interests of the students taking the course.

Grading and Examination Policies
30% of the grade will be based on homework assignments, 30% on the midterm exam, and 40% on the final exam.
Homework will be assigned in class approximately every two weeks. You are encouraged to discuss homework problems with classmates. However, you are not allowed to copy other people's work. Some selected problems will be graded by the instructor, but most of them will be only checked for completeness. Solutions to homework problems can be provided upon student's request.
The (one hour) midterm exam will be given in regular class time on Oct. 12th, Friday. It will be open book, open notes, but noncooperative.
The final exam will be take-home, which will be handed out two weeks before the semester ends. You are not permitted to discuss the problems with others.

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.