On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 2, pp. 559-574.

Les auteurs de l'article [Probab. Theory Related Fields 141 (2008) 543-567] ont prouvé un résultat d'unicité pour les solutions d'EDSRs quadratiques de générateur convexe et de condition terminale non bornée ayant tous leurs moments exponentiels finis. Dans ce papier, nous prouvons que ce résultat d'unicité reste vrai pour des solutions qui admettent uniquement certains moments exponentiels finis. Ces moments exponentiels sont reliés de manière naturelle à ceux présents dans le théorème d'existence. À l'aide de ce résultat d'unicité nous pouvons améliorer la formule de Feynman-Kac non linéaire prouvée dans [Probab. Theory Related Fields 141 (2008) 543-567].

In [Probab. Theory Related Fields 141 (2008) 543-567], the authors proved the uniqueness among the solutions of quadratic BSDEs with convex generators and unbounded terminal conditions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved in [Probab. Theory Related Fields 141 (2008) 543-567].

DOI : 10.1214/10-AIHP372
Classification : 60H10
Mots-clés : backward stochastic differential equations, generator of quadratic growth, unbounded terminal condition, uniqueness result, nonlinear Feynman-Kac formula 
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     author = {Delbaen, Freddy and Hu, Ying and Richou, Adrien},
     title = {On the uniqueness of solutions to quadratic {BSDEs} with convex generators and unbounded terminal conditions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {559--574},
     publisher = {Gauthier-Villars},
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     number = {2},
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     doi = {10.1214/10-AIHP372},
     mrnumber = {2814423},
     zbl = {1225.60093},
     language = {en},
     url = {http://www.numdam.org/articles/10.1214/10-AIHP372/}
}
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Delbaen, Freddy; Hu, Ying; Richou, Adrien. On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 2, pp. 559-574. doi : 10.1214/10-AIHP372. http://www.numdam.org/articles/10.1214/10-AIHP372/

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