Mean-field backward stochastic differential equations with mean reflection and nonlinear resistance

TL;DR

This paper investigates the existence and uniqueness of solutions for mean-field backward stochastic differential equations with mean reflection and nonlinear resistance, and applies these results to a super-hedging problem with risk constraints.

Contribution

It introduces a novel approach combining contraction mapping, stitching, and fixed point methods to establish well-posedness of complex mean-field BSDEs with mean reflection.

Findings

Existence of a unique local solution on small time intervals.

Global solutions constructed via a two-step stitching and fixed point approach.

Application to super-hedging with risk constraints.

Abstract

The present paper is devoted to the study of the well-posedness of mean field BSDEs with mean reflection and nonlinear resistance. By the contraction mapping argument, we first prove that the mean-field BSDE with mean reflection and nonlinear resistance admits a unique deterministic flat local solution on a small time interval. Moreover, we build the global solution by introducing a two-step approach, which is a combination of stitching method and fixed point method. We further provide an application to the super-hedging problem with risk constraint.