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A Generalized Comparison Theorem for BSDEs and Its Applications

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Abstract

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).

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Authors and Affiliations

  1. College of Sciences, China University of Mining & Technology, Xuzhou, Jiangsu, 221116, P.R. China

    Sheng-Jun Fan & Long Jiang

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  1. Sheng-Jun Fan
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  2. Long Jiang
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Correspondence to Sheng-Jun Fan.

Additional information

Supported by the National Natural Science Foundation of China (No. 10671205), National Basic Research Program of China (No. 2007CB814901), Youth Foundation of China University of Mining & Technology (No. 2006A041 and No. 2007A029), and Qing Lan Project.

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Fan, SJ., Jiang, L. A Generalized Comparison Theorem for BSDEs and Its Applications. J Theor Probab 25, 50–61 (2012). https://doi.org/10.1007/s10959-010-0293-8

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