Independent work involving experiments, computer programming, analytical investigation, or engineering design.
Independent work involving experiments, computer programming, analytical investigation, or engineering design.
Selected topics of interest in the area of quantitative finance. Offerings vary each year; some topics include energy derivatives, experimental finance, foreign exchange and related derivative instruments, inflation derivatives, hedge fund management, modeling equity derivatives in Java, mortgage-backed securities, numerical solutions of partial differential equations, quantitative portfolio management, risk management, trade and technology in financial markets.
Stochastic control has broad applications in almost every walk of life, including finance, revenue management, energy, health care and robotics. Classical, model-based stochastic control theory assumes that the system dynamics and reward functions are known and given, whereas modern, model-free stochastic control problems call for reinforcement learning to learn optimal policies in an unknown environment. This course covers model-based stochastic control and model-free reinforcement learning, both in continuous time with continuous state space and possibly continuous control (action) space. It includes the following topics: Shortest path problem, calculus of variations and optimal control; formulation of stochastic control; maximum principle and backward stochastic differential equations; dynamic programming and Hamilton-Jacobi-Bellman (HJB) equation; linear-quadratic control and Riccati equations; applications in high-frequency trading; exploration versus exploitation in reinforcement learning; policy evaluation and martingale characterization; policy gradient; q-learning; applications in diffusion models for generative AI.
Prerequisite(s): Approval by a faculty member who agrees to supervise the work. Independent work involving experiments, computer programming, analytical investigation, or engineering design.
Prerequisite(s): Approval by a faculty member who agrees to supervise the work. Independent work involving experiments, computer programming, analytical investigation, or engineering design.
Before registering, the student must submit an outline of the proposed work for approval by the supervisor and the chair of the Department. Advanced study in a specialized field under the supervision of a member of the department staff. May be repeated for credit.