Stochastic maximum principle for optimal control problem of non exchangeable mean field systems
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.
Fields of Study & Subjects
Stochastic processes and financial applications
Stability and Controllability of Differential Equations
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Mathematical Control and Related Fields
- Volume
- 0
- Issue
- 0
- Publication date
- 1 January 2026
- Language
- EN