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

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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)

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.

Suggested Citation

  • Anna de Crescenzo & Filippo de Feo & Huyên Pham, 2025. "Linear-quadratic optimal control for non-exchangeable mean-field SDEs and applications to systemic risk," Working Papers hal-04975940, HAL.
    • Handle: RePEc:hal:wpaper:hal-04975940
    Note: View the original document on HAL open archive server: https://hal.science/hal-04975940v2
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