On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions

被引：59
|
作者：
Delbaen, Freddy [1 ]
Hu, Ying [2 ]
Richou, Adrien [2 ]
机构：
[1] ETH Zentrum, Dept Math, CH-8092 Zurich, Switzerland
[2] Univ Rennes 1, IRMAR, F-35042 Rennes, France
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2011年 / 47卷 / 02期
关键词：
Backward stochastic differential equations; Generator of quadratic growth; Unbounded terminal condition; Uniqueness result; Nonlinear Feynman-Kac formula; STOCHASTIC DIFFERENTIAL-EQUATIONS; GROWTH;
D O I：
10.1214/10-AIHP372
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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].
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页码：559 / 574
页数：16
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