## Electronic Communications in Probability

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

#### Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1536718012

Digital Object Identifier
doi:10.1214/18-ECP166

Mathematical Reviews number (MathSciNet)
MR3863915

Zentralblatt MATH identifier
06964402

#### Citation

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

#### References

• [1] Briand, P., Delyon, B., Hu, Y., Pardoux, E. and Stoica, L.: $L^p$ solutions of backward stochastic differential equations. Stochastic Process. Appl. 108, (2003), 109–129.
• [2] Briand, P. and Hu,Y.: BSDE with quadratic growth and unbounded terminal value. Probab. Theory Related Fields 136, (2006), 604–618.
• [3] Delbaen, F., Hu, Y. and Richou, A.: On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions. Ann. Inst. Henri Poincaré Probab. Stat. 47, (2011), 559–574.
• [4] El Karoui, N., Peng, S. and Quenez, M. C.: Backward stochastic differential equations in finance. Math. Finance 7, (1997), 1–71.
• [5] Hu, Y. and Tang, S.: Existence of solution to scalar BSDEs with $L\exp \!{\left (\!\sqrt {{2\over \lambda }\log {(1+L)}}\,\right )}$-integrable terminal values. Electron. Commun. Probab. 23, (2018), Paper No. 27, 11pp.
• [6] Lepeltier, J. P. and San Martin, J.: Backward stochastic differential equations with continuous coefficient. Statist. Probab. Lett. 32, (1997), 425–430.
• [7] Pardoux, E. and Peng, S.: Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14, (1990), 55–61.