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

Anna de Crescenzo (), Filippo de Feo () and Huyên Pham ()
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Anna de Crescenzo: UPCité - Université Paris Cité, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité
Filippo de Feo: Institut für Mathematik [Berlin] - TUB - Technical University of Berlin / Technische Universität Berlin
Huyên Pham: X - École polytechnique - IP Paris - Institut Polytechnique de Paris, CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: graphons; Mean-field SDE; systemic risk.; MSC Classification: 49N10 49N82 93E20 Mean-field SDE heterogeneous interaction graphons linear quadratic optimal control Riccati system systemic risk; MSC Classification: 49N10; 49N82; 93E20 Mean-field SDE; heterogeneous interaction; linear quadratic optimal control; systemic risk; Riccati system (search for similar items in EconPapers)
Date: 2025-12-16
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