Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values

Ying Hu (1) , Shanjian Tang (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 SCHOOL OF MATHEMATICAL SCIENCES - School of Mathematical Sciences

In this paper, we study a scalar linearly growing BSDE with a weakly $L^{1+}$-integrable terminal value. We prove that the BSDE admits a solution if the terminal value satisfies some $\Psi$-integrability condition, which is weaker than the usual $L^p$ ($p>1$) integrability and stronger than $L\log L$ integrability. We show by a counterexample that $L\log L$ integrability is not sufficient for the existence of solution to a BSDE of a linearly growing generator.

Domaines: Probabilités [math.PR]

Ying Hu, Shanjian Tang. Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values. 2017. ⟨hal-01507371v2⟩