A uniqueness theorem for solution of BSDEs

TL;DR

This paper proves a uniqueness theorem for solutions of backward stochastic differential equations (BSDEs) when the generator function is uniformly continuous in z, independent of y, and uniformly continuous in (ω,t).

Contribution

It establishes a new uniqueness result for BSDE solutions under conditions of uniform continuity and independence from y.

Findings

Uniqueness of BSDE solutions under specified conditions

Generator g's uniform continuity in z ensures solution uniqueness

Independence of g from y is crucial for the result

Abstract

In this note, we prove that if $g$ is uniformly continuous in $z$, uniformly with respect to $(\oo,t)$ and independent of $y$, the solution to the backward stochastic differential equation (BSDE) with generator $g$ is unique.