Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: The critical case

Pages: 5273 - 5283, Volume 35, Issue 11, November 2015      doi:10.3934/dcds.2015.35.5273

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Freddy Delbaen - Department of Mathematics, ETH-Zentrum, HG G 54.3, CH-8092 Zürich, Switzerland (email)
Ying Hu - IRMAR, Université Rennes 1, Campus de Beaulieu, F-35042 Rennes Cedex, France (email)
Adrien Richou - Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France (email)

Abstract: In F. Delbaen, Y. Hu and A. Richou (Ann. Inst. Henri Poincaré Probab. Stat. 47(2):559--574, 2011), the authors proved that uniqueness of solution to quadratic BSDE with convex generator and unbounded terminal condition holds among solutions whose exponentials are $L^p$ with $p$ bigger than a constant $\gamma$ ($p>\gamma$). In this paper, we consider the critical case: $p=\gamma$. We prove that the uniqueness holds among solutions whose exponentials are $L^\gamma$ under the additional assumption that the generator is strongly convex. These exponential moments are natural as they are given by the existence theorem.

Keywords:  Quadratic BSDEs, convex generators, unbounded terminal conditions, critical case, uniqueness.
Mathematics Subject Classification:  60H10.

Received: March 2013;      Revised: March 2014;      Available Online: May 2015.