On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions
Delbaen, Freddy ; Hu, Ying ; Richou, Adrien
Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, p. 559-574 / Harvested from Project Euclid
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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].
Publié le : 2011-05-15
Classification:  Backward stochastic differential equations,  Generator of quadratic growth,  Unbounded terminal condition,  Uniqueness result,  Nonlinear Feynman–Kac formula,  60H10 
@article{1300887282,
     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 = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {47},
     number = {1},
     year = {2011},
     pages = { 559-574},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1300887282}
}

Delbaen, Freddy; Hu, Ying; Richou, Adrien. On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions. Ann. Inst. H. Poincaré Probab. Statist., Tome 47 (2011) no. 1, pp.  559-574. http://gdmltest.u-ga.fr/item/1300887282/