A Generalized Comparison Theorem for BSDEs and Its Applications

Sheng-Jun Fan () and Long Jiang ()
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Sheng-Jun Fan: China University of Mining & Technology
Long Jiang: China University of Mining & Technology

Journal of Theoretical Probability, 2012, vol. 25, issue 1, 50-61

Abstract: 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).

Keywords: Backward stochastic differential equation; Comparison theorem; Uniformly continuous generator; Monotonic generator; 60H10 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-010-0293-8

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