Columbia & NYU Financial Engineering Colloquium: Huyen Pham

Huyen Pham

Professor, École Polytechnique

Title

Control of large-scale heterogeneous systems: an extended graphon mean-field approach

Abstract

Networks play a central role in modeling complex systems such as financial markets, power grids, social interactions, and epidemiology. As these systems scale in size and complexity, understanding their behavior requires scalable and robust methodologies. This talk examines dynamical systems of interacting agents/particles with heterogeneous connections, described by graph structures. By employing graphon theory, we analyze the large-population limit, proving a propagation of chaos result that yields a collection of mean-field stochastic differential equations.

We further address the control of these non-exchangeable McKean-Vlasov systems from the perspective of a central planner capable of influencing asymmetric interactions. Leveraging tools tailored for this framework, such as derivatives along flows of measures and the corresponding Itô calculus, we establish that the value function of this control problem satisfies a Bellman dynamic programming equation in a function space over the Wasserstein space.

To illustrate the applicability of our approach, we present a linear-quadratic graphon model with analytical solutions and apply it to a systemic risk example involving heterogeneous banks.

Based on joint works with: A. De Crescenzo, F. Coppini, F. De Feo, M. Fuhrman and I. Kharroubi.