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

Abstract

In [4], the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) if the terminal value is $L\exp{\left(μ\sqrt{2\log{(1+L)}}\,\right)}$-integrable with the positive parameter $μ$ being bigger than a critical value $μ\_0$. In this note, we give the uniqueness result for the preceding BSDE.