Time and location: WF 9:00am – 10:15am, KAP 245. 

Instructor: Jianfeng Zhang, KAP 248E, (213)7409805 

Email: jianfenz@usc.edu Homepage: http://almaak.usc.edu/~jianfenz 

Office hours: WF 10:15am-11:45am, or by appointment, in KAP 248 E 

Textbook: Backward Stochastic Differential Equations — from linear to fully nonlinear theory, by Jianfeng Zhang, Springer 2017. 

Course Description: 

Stochastic controls/games has been a major branch of stochastic analysis, and it is also one of the central topics in economics (typically in discrete models). In the first part of the course, we will study the case with drift control only. In this case, we will focus on various formulations of the problems and their economic implications. In particular, for the games (including zero sum game, nonzero sum game, principal agent problems), we will see the problems are extremely sensitive to the information setting. One major tool in this case is the backward SDE.

In the second part of the course, we will consider the case with diffusion control, which is also closely related to the robust analysis for economic/financial models with volatility uncertainty. The problem becomes a lot more challenging in this case. We shall introduce the mathematical tools developed in recent years, including the quasi sure stochastic analysis, nonlinear expectation, second order backward SDEs, as well as path dependent PDEs. We will show their connection to the standard tools like dynamic programming principle and Hamilton-Jacobi-Bellman equations.

We will also cover the optimal stopping problem, whose control is a stopping time. One typical application of this problem is the American option pricing. If time allows, we will introduce briefly the mean field games, which has received very strong attention in recent years.  

Grading and Examination Policies 

40% of the grade will be based on homework assignments, 60% on class participation, including the final presentation. 

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. Solutions to homework problems can be provided upon students’ request.

Each student will be required to give a presentation on related topics. Details will be discussed in class.

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.

Statement for Students with Disabilities 

Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me (or to TA) as early in the semester as possible. DSP is located in STU 301 and is open 8:30 a.m.-5:00 p.m., Monday through Friday. The phone number for DSP is (213) 740-0776.

Statement on Academic Integrity 

USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect one’s own academic work from misuse by others as well as to avoid using another’s work as one’s own. All students are expected to understand and abide by these principles. Scampus, the Student Guidebook, contains the Student Conduct Code in Section 11.00, while the recommended sanctions are located in Appendix A: http://www.usc.edu/dept/publications/SCAMPUS/gov/. Students will be referred to the Office of Student Judicial Affairs and Community Standards for further review, should there be any suspicion of academic dishonesty. The Review process can be found at: http://www.usc.edu/student-affairs/SJACS/.