Time and location:  W F 9-10:15am, the course is online

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

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

Office hours:  W F 10:15-11:45 or by appointment (the office hour is also online. Email me if you need the Zoom link information)

Recommended Book (optional, and other materials will be added later):  Backward Stochastic Differential Equations — from linear to fully nonlinear theory, by Jianfeng Zhang, Springer 2017. 

Prerequisites: Math 509 (or approval from the instructor). The course will be measure theory based, and basic knowledge on Brownian motions, martingale theory, Markov property, and stochastic differential equations will be needed.

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). The course will consists of three parts.

In the first part we will study stochastic control problems. We will use the dynamic programming principle approach to derive the HJB equation. We will also discuss both open loop and closed loop controls, and for the open loop controls we will also introduce the stochastic maximum principle.

In the second part we will study a few games, including zero sum game, nonzero sum game, and principal agent problems. We will see that the games are extremely sensitive to the information setting. One major tool in this case is the backward SDE.

In the last part we will give a brief introduction on the mean field controls and mean field games, which have received very strong attention in the 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 (at Zoom). You can also schedule one-to-one Zoom meeting with me.

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/.