Linear-quadratic optimal control for non-exchangeable mean-field SDEs and applications to systemic risk

¹ LPSM, Université Paris Cité and Sorbonne University, Paris, France
² Institut für Mathematik, Technische Universität Berlin, Berlin, Germany and Department of Economics and Finance, Luiss Guido Carli University, Rome, Italy
³ Ecole Polytechnique, CMAP, Paris, France

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 6 March 2025
Accepted: 27 February 2026

Abstract

We study the linear-quadratic control problem for a class of non-exchangeable mean-field systems, which model large populations of heterogeneous interacting agents. We explicitly characterize the optimal control in terms of a new infinite-dimensional system of Riccati equations, for which we establish existence and uniqueness. To illustrate our results, we apply this framework to a systemic risk model involving heterogeneous banks, demonstrating the impact of agent heterogeneity on optimal risk mitigation strategies.