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arXiv · 2503.03318

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

Anna de Crescenzo·Filippo de Feo·Huyên Pham
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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.

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Anna de Crescenzo, Filippo de Feo, Huyên Pham. 2025-12-29. Linear-quadratic optimal control for non-exchangeable mean-field SDEs and applications to systemic risk. https://arxiv.org/abs/2503.03318

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