With the availability of high frequency financial data, new areas of research in stochastic modeling and stochastic control have opened up. This six-week course will introduce students to the basic concepts, questions, and methods that arise in this domain. We will begin with the classical market microstructure models, understand different theories of price formation and price discovery, identify different types of market participants, and then move on to reduced form models. Next, we will investigate some of the typical algorithmic trading strategies employed in industry for different asset classes. Finally, we will develop stochastic optimal control problems for solving optimal liquidation and high frequency market making problems and demonstrate how to solve those problems using the principles of dynamic programming leading to Hamilton-Jacobi-Bellman equations. Students will also have a chance to work with historical limit order book data, develop Monte Carlo simulations and gain a working knowledge of the models and methods. and methods.

Tentative topics include: Market Microstructure; Overview of Stochastic Calculus; Dynamic Programming & HJB -Dynamics of LOB-Optimal Liquidation; Market Making; Risk Measures.