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

2025/03/05 by de Crescenzo, Anna, de Feo, Filippo, Pham, Huyên · 3 citations
#FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.03318

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.

Cited by

• An Overview of Some Extensions of Mean Field Games beyond Perfect Homogeneity and Anonymity
• Contracting a crowd of heterogeneous agents
• Stochastic maximum principle for optimal control problem of non exchangeable mean field systems

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