General Information
The goal of this course is to develop, implement, and present small-group research projects on topics in mathematical finance. The first half of the course will be devoted to learning relevant background material including Brownian motion, Ito calculus, the Feynman-Kacs PDE (connecting probability to PDEs for pricing derivatives), and the Hamilton-Jacobi-Bellman PDE (connecting probability to PDEs to describe optimal investment problems).
The course themes will vary from semester to semester. Some possible themes include universal basic income welfare models in a financial equilibrium, financial modeling with jumps, the rise and use of trading platform apps, using backward stochastic differential equations for financial optimization problems, market microstructure, modeling of mortgages, and sports betting.
Throughout the first half of the course, the mathematical setting for the theme will be covered in enough detail to be a launching pad for the research projects. Each group's specific research project topic will be based on the broader theme and will be generated in collaboration with the instructor and the group. The second half of the course will be devoted to implementing and executing the research projects. The students will present their work to the class in the final two weeks of the semester.
Prerequisites
- 01:640:485.
- Alternatively, 01:640:477 with grade of B+ or A.
To register using the alternative prerequisites, fill out this form.
Textbook
We will not follow a specific textbook, so you are encouraged to take notes in class. Supplementary material will be posted to our course's Canvas site.