Construction and Uniqueness for reflected BSDE under linear increasing condition

TL;DR

This paper investigates the existence and uniqueness of solutions for reflected backward stochastic differential equations (BSDEs) with one or two barriers, under a generator with a continuous and linearly increasing condition.

Contribution

It introduces a construction method for solutions of reflected BSDEs with barriers and establishes their uniqueness under linear increasing generator conditions.

Findings

Established construction methods for reflected BSDE solutions.

Proved uniqueness of solutions under linear increasing generator conditions.

Extended understanding of reflected BSDEs with multiple barriers.

Abstract

In this paper, we study the uniqueness of the solution of reflected BSDE with one or two barriers, under continuous and linear increasing condition of generator $g$. Before that we study the construction of solution of of reflected BSDE with one or two barriers.