Electronic Communications in Probability

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

Rainer Buckdahn, Ying Hu, and Shanjian Tang

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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.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 59, 8 pp.

Received: 16 May 2018
Accepted: 24 August 2018
First available in Project Euclid: 12 September 2018

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]

backward stochastic differential equation $L\exp{(\mu \sqrt {2\log {(1+L)}}\,)} $ integrability uniqueness

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Buckdahn, Rainer; Hu, Ying; Tang, Shanjian. Uniqueness of solution to scalar BSDEs with $L\exp{\left (\mu \sqrt {2\log {(1+L)}}\,\right )} $-integrable terminal values. Electron. Commun. Probab. 23 (2018), paper no. 59, 8 pp. doi:10.1214/18-ECP166. https://projecteuclid.org/euclid.ecp/1536718012

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