On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case

Abstract

In [3], the authors proved that uniqueness holds among solutions whose exponentials are $L^p$ with $p$ bigger than a constant $\gamma$ ($p\textgreater{}γ$). In this paper, we consider the critical case: $p=\gamma$. We prove that the uniqueness holds among solutions whose exponentials are $L^{\gamma }$ under the additional assumption that the generator is strongly convex.