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A comonotonic theorem for BSDEs. (English) Zbl 1070.60050

Summary: E. Pardoux and S. G. Peng [Syst. Control Lett. 14, 55–61 (1990; Zbl 0692.93064)] introduced a class of nonlinear backward stochastic differential equations (BSDEs). According to Pardoux and Peng’s theorem, the solution of this type of BSDE consists of a pair of adapted processes, say (\(y,z\)). Since then, many researchers have been exploring the properties of this pair solution (\(y,z\)), especially the properties of the first part \(y\). In this paper, we shall explore the properties of the second part \(z\). A comonotonic theorem with respect to \(z\) is obtained. As an application of this theorem, we prove an integral representation theorem of the solution of BSDEs.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Citations:

Zbl 0692.93064
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References:

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