Skorohod equation and BSDE's with two reflecting barriers

TL;DR

This paper extends the theory of doubly reflected backward stochastic differential equations (BSDEs) by incorporating generator dependence on reflection resistance, proving existence, uniqueness, and continuous dependence.

Contribution

It introduces a novel class of doubly reflected BSDEs with generator dependence on reflection resistance, extending prior work on single-barrier reflected BSDEs.

Findings

Established existence and uniqueness of solutions.

Proved continuous dependence on parameters.

Extended previous models to include reflection resistance dependence.

Abstract

We solve a class of doubly reflected backward stochastic differential equation whose generator depends on the resistance due to reflections, which extend the recent work of Qian and Xu on reflected BSDE with one barrier. We then obtain the existence and uniqueness and the continuous dependence theorem for this reflected BSDE.