Tianjiao Hua, Peng Luo
Published 2024-03-21Version 1
In this paper, we study a class of infinite horizon fully coupled McKean-Vlasov forward-backward stochastic differential equations (FBSDEs). We propose a generalized monotonicity condition involving two flexible functions. Under this condition, we establish the well-posedness results for infinite horizon McKean-Vlasov FBSDEs by the method of continuation, including the unique solvability, an estimate of the solution, and the related continuous dependence property of the solution on the coefficients. Based on the solvability result, we study an infinite horizon mean field control problem. Moreover, by choosing appropriate form of the flexible functions, we can eliminate the different phenomenon between the linear-quadratic (LQ) problems on infinite horizon and finite horizon proposed in Wei and Yu (SIAM J. Control Optim. 59: 2594-2623, 2021).
Solvability of Infinite horizon McKean-Vlasov FBSDEs in Mean Field Control Problems and Games
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Case
Deep Galerkin Method for Mean Field Control Problem
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