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

Rainer Buckdahn (1) , Ying Hu (2) , Shanjian Tang (3)

1 LM - Laboratoire de mathématiques de Brest
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 SCHOOL OF MATHEMATICAL SCIENCES - School of Mathematical Sciences

In [4], the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) if the terminal value is $L\exp{\left(\mu \sqrt{2\log{(1+L)}}\,\right)}$-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.

Domaines: Probabilités [math.PR]

Rainer Buckdahn, Ying Hu, Shanjian Tang. Uniqueness of solution to scalar BSDEs with $L\exp{\left(\mu \sqrt{2\log{(1+L)}}\,\right)}$-integrable terminal values. Electronic Communications in Probability, 2018, 23 (paper n°59), 8p. ⟨10.1214/18-ECP166⟩. ⟨hal-01793086⟩