TOPICS IN QUANT FINANCE

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.