On the uniqueness of solutions to quadratic BSDEs with non-convex generators

TL;DR

This paper establishes uniqueness results for quadratic backward stochastic differential equations without convexity assumptions, including new findings for unbounded cases with path-dependent terminal conditions and generators.

Contribution

It provides the first known uniqueness results for quadratic BSDEs without convexity, extending to unbounded cases with path-dependent data.

Findings

Uniqueness results for quadratic BSDEs without convexity

Strong estimates on the Z process for unbounded cases

Applicability to path-dependent terminal conditions

Abstract

In this paper we prove some uniqueness results for quadratic backward stochastic differential equations without any convexity assumptions on the generator. The bounded case is revisited while some new results are obtained in the unbounded case when the terminal condition and the generator depend on the path of a forward stochastic differential equation. Some of these results are based on strong estimates on $Z$ that are interesting on their own and could be applied in other situations.