Mathematics Colloquium: Adaptive-Robust Stochastic Control with Applications to Financial Markets

Speaker:  Igor Cialenco, Illinois Institute of Technology

Title:  Adaptive-Robust Stochastic Control with Applications to Financial Markets

Abstract:  Motivated by various real-world problems, we propose a new methodology, called adaptive-robust control, for solving a discrete-time stochastic control problem subject to model uncertainty, also known as Knightian uncertainty. The uncertainty comes from the fact that the controller does not know the true probability law of the underlying model but only that it belongs to a certain family of probability laws. We develop a learning algorithm that reduces the model uncertainty through progressive learning about the unknown system. One of the key components in the proposed methodology is the recursive construction of the confidence sets for the unknown parameters of a general ergodic Markov process. This, in particular, allows to establish the Bellman system of equations corresponding to the original stochastic control problem.

This general stochastic control framework will be applied to a classical finance problem of allocating wealth optimally across several risky assets, also known as optimal portfolio allocation problem. We will discuss both time-consistent and time-inconsistent terminal Markovian control problems. Finally, we provide a machine learning algorithm in solving numerically some of these problems, such as the dynamic Markowitz mean-variance portfolio selection problem with the modern twist of model uncertainty. 

Time:  Friday, April 8, 2022, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

In-person and on Zoom