We prove a uniqueness result of the unbounded solution for a quadratic backward stochastic differential equation whose terminal condition is unbounded and whose generator may be non-Lipschitz continuous in the state variable and non-convex (non-concave) in the state variable , and instead satisfies a strictly quadratic condition and an additional assumption. The key observation is that if the generator is strictly quadratic, then the quadratic variation of the first component of the solution admits an exponential moment. Typically, a Lipschitz perturbation of some convex (concave) function satisfies the additional assumption mentioned above. This generalizes some results obtained in [1] and [2].
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@article{CRMATH_2020__358_2_227_0,
author = {Fan, Shengjun and Hu, Ying and Tang, Shanjian},
title = {On the uniqueness of solutions to quadratic {BSDEs} with non-convex generators and unbounded terminal conditions},
journal = {Comptes Rendus. Math\'ematique},
pages = {227--235},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {2},
year = {2020},
doi = {10.5802/crmath.40},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.40/}
}
TY - JOUR AU - Fan, Shengjun AU - Hu, Ying AU - Tang, Shanjian TI - On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions JO - Comptes Rendus. Mathématique PY - 2020 SP - 227 EP - 235 VL - 358 IS - 2 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.40/ DO - 10.5802/crmath.40 LA - en ID - CRMATH_2020__358_2_227_0 ER -
%0 Journal Article %A Fan, Shengjun %A Hu, Ying %A Tang, Shanjian %T On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions %J Comptes Rendus. Mathématique %D 2020 %P 227-235 %V 358 %N 2 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.40/ %R 10.5802/crmath.40 %G en %F CRMATH_2020__358_2_227_0
Fan, Shengjun; Hu, Ying; Tang, Shanjian. On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions. Comptes Rendus. Mathématique, Tome 358 (2020) no. 2, pp. 227-235. doi : 10.5802/crmath.40. http://www.numdam.org/articles/10.5802/crmath.40/
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