A Generalized Comparison Theorem for BSDEs and Its Applications

作者：Fan, Sheng Jun^*; Jiang, Long

来源：Journal of Theoretical Probability, 2012, 25(1): 50-61.

DOI：10.1007/s10959-010-0293-8

• Backward stochastic differential equation
• Comparison theorem
• Uniformly continuous generator
• Monotonic generator

This paper establishes a generalized comparison theorem for one-dimensional backward stochastic differential equations (BSDEs) whose generators are uniformly continuous in z and satisfy a kind of weakly monotonic condition in y. As applications, two new existence and uniqueness theorems for solutions of BSDEs are obtained. In the one-dimensional setting, these results generalize some corresponding results in Pardoux and Peng (Syst. Control Lett. 14:55-61, 1990), Mao (Stoch. Process. Their Appl. 58:281-292, 1995), El Karoui et al. (Math. Finance 7:1-72, 1997), Pardoux (Nonlinear Analysis, Differential Equations and Control, Montreal, QC, 1998, Kluwer Academic, Dordrecht, 1999), Cao and Yan (Adv. Math. 28(4):304-308, 1999), Briand and Hu (Probab. Theory Relat. Fields 136(4):604-618, 2006), and Jia (C. R. Acad. Sci. Paris, Ser. I 346:439-444, 2008).

• 出版日期2012-3
• 单位中国矿业大学（北京）