Quadratic BSDEs with convex generators and unbounded terminal conditions
Quadratic BSDEs with convex generators and unbounded terminal conditions
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DOI：
10.1007/s00440-007-0093-y
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发表时间：
2007-03
影响因子：
2
通讯作者：
P. Briand;Ying Hu
中科院分区：
文献类型：
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作者：
P. Briand;Ying Hu
在Briand和Hu（Probab Theory Relat Fields 136（4）：604-618，2006）中，作者证明了具有关于变量z的二次生成元的BSDE的存在性结果，并且具有无界终端条件。然而，在这项工作中没有唯一性结果。本文的主要目标就是填补这一空白。为了得到这类倒向随机微分方程的比较定理，我们假设生成元关于变量z是凸的。根据这一假设的凸性，我们也能够证明一个稳定的结果在精神的先验估计在Karoui等人。(Math Finance 7（1）：1-71，1997）。有了这些工具，我们可以推导出非线性Feynman-Kac公式。
In Briand and Hu (Probab Theory Relat Fields 136(4):604–618, 2006), the authors proved an existence result for BSDEs with quadratic generators with respect to the variablezand with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variablez. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in Karoui et al. (Math Finance 7(1):1–71, 1997). With these tools in hands, we can derive the nonlinear Feynman–Kac formula in this context.