Mean-Field Backward Stochastic Differential Equations with Nonlinear Resistance and Double Mean Reflections

TL;DR

This paper studies advanced mean-field backward stochastic differential equations with double mean reflections and nonlinear resistance, establishing existence and uniqueness results for various generator conditions.

Contribution

It introduces new formulations of MFBSDEs with double mean reflections and nonlinear resistance, proving well-posedness under different generator assumptions.

Findings

Proved existence and uniqueness for Lipschitz generators.

Extended results to quadratic generators with bounded terminal value.

Analyzed well-posedness of a variant with absolutely continuous compensating term.

Abstract

In this paper, we investigate mean-field backward stochastic differential equation (MFBSDE) with double mean reflections and nonlinear resistance. Specifically, the constraints are formulated in terms of the expectation of the solution, and a compensating term is incorporated into the generator. We establish the existence and uniqueness for both the case of Lipschitz generator and the case where the generator is quadratic and the terminal value is bounded. Finally, when the compensating term is absolutely continuous, we study the well-posedness of a variant type of doubly mean reflected MFBSDE with nonlinear resistance, whose generator depends on the density function of the compensating term.