Uniqueness of solution to scalar BSDEs with $L\exp{\left (\mu \sqrt {2\log {(1+L)}}\,\right )} $-integrable terminal values

Abstract

In [5], the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) if the terminal value is $L\exp \hskip -0.5pt{\left (\mu \sqrt{2\log {(1+L)}} \right )}\hskip -0.5pt$-integrable with the positive parameter $\mu $ being bigger than a critical value $\mu _0$. In this note, we give the uniqueness result for the preceding BSDE.