Stochastic maximum principle for optimal control problem of non exchangeable mean field systems

2025/06/05 by Kharroubi, Idris, Mekkaoui, Samy, Pham, Huyên · 1 citation
#49N80 #60K35 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.05595

Abstract

We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric couplings. Our analysis leads to a collection of forward-backward stochastic differential equations (FBSDE) of non exchangeable mean field type. Under suitable assumptions, we establish the solvability of this system. As an illustration, we consider the linear-quadratic case, where the optimal control is characterized by an infinite dimensional system of Riccati equations.

Citations

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Cited by

• A non-exchangeable mean field control problem with controlled interactions

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