Propagation of Chaos for Doubly Mean Reflected BSDEs

Abstract

Abstract In this paper, we establish propagation of chaos (POC) for doubly mean reflected backward stochastic differential equations (MRBSDEs). MRBSDEs differ from typical RBSDEs in that the constraint is not on the paths of the solution but on its law. We focus on approximating MRBSDEs by interacting particle systems (IPS) and achieve distinct convergence speeds under different scenarios. We propose two sets of IPS having mean-field Skorokhod problems, capturing the dynamics of IPS reflected in a mean-field way. As the dimension of the IPS tends to infinity, the system converges to a limit with independent particles, where each solves the MRBSDE.