Stochastic Systems and Learning Theory with Applications in Finance

The first half of this course provides a rigorous introduction to the foundations of stochastic systems and control theory in discrete-time. The second half explores the associated applications in machine learning theory, with a particular emphasis on reinforcement learning and generative diffusion models. Throughout the course, financial applications will be a central theme, including topics such as algorithmic trading (optimal execution, portfolio optimization, and smart order routing), reinforcement learning for market making, and the generation of financial scenarios and time series using diffusion-based generative models.