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2019 Existence and uniqueness of solution to scalar BSDEs with $L\exp (\mu \sqrt{2\log (1+L)} )$-integrable terminal values: the critical case
Shengjun Fan, Ying Hu
Electron. Commun. Probab. 24: 1-10 (2019). DOI: 10.1214/19-ECP254

Abstract

In [8], the existence of the solution is proved for a scalar linearly growingbackward stochastic differential equation (BSDE) when the terminal value is$L\exp (\mu \sqrt{2\log (1+L)} )$-integrable for a positive parameter $\mu >\mu _{0}$ with a critical value $\mu _{0}$, and a counterexample is provided to show that the preceding integrability for $\mu <\mu _{0}$ is not sufficient to guarantee the existence of the solution. Afterwards, the uniqueness result (with $\mu >\mu _{0}$) is also given in [3] for the preceding BSDE under the uniformly Lipschitz condition of the generator. In this note, we prove that these two results still hold for the critical case: $\mu =\mu _{0}$.

Citation

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Shengjun Fan. Ying Hu. "Existence and uniqueness of solution to scalar BSDEs with $L\exp (\mu \sqrt{2\log (1+L)} )$-integrable terminal values: the critical case." Electron. Commun. Probab. 24 1 - 10, 2019. https://doi.org/10.1214/19-ECP254

Information

Received: 4 April 2019; Accepted: 2 July 2019; Published: 2019
First available in Project Euclid: 12 September 2019

zbMATH: 1422.60094
MathSciNet: MR4003123
Digital Object Identifier: 10.1214/19-ECP254

Subjects:
Primary: 60H10

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