Speaker: Anna De Crescenzo
Title: Heterogeneous mean-field systems
Abstract: We study the optimal control of mean-field systems with heterogeneous interactions. 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. 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 F. Coppini, F. de Feo, M. Fuhrman, I. Kharroubi, H. Pham.