Jensen’s inequality for backward stochastic differential equations. (English) Zbl 1109.60042

Summary: Under the Lipschitz assumption and square integrable assumption on \(g\), the author proves that Jensen’s inequality holds for backward stochastic differential equations with generator \(g\) if and only if \(g\) is independent of \(y,g(t,0)\equiv 0\) and \(g\) is super-homogeneous with respect to \(z\). This result generalizes the known results on Jensen’s inequality for \(g\)-expectation in [P. Briand, F. Coquet, Y. Hu, J. Mémin and S. Peng, Electron. Commun. Probab. 5, 101–117 (2000; Zbl 0966.60054); Z. Chen, R. Kulperger and L. Jiang, C. R. Math., Acad. Sci. Paris 337, No. 11, 725–730 (2003; Zbl 1031.60014) and ibid. 337, No. 12, 797–800 (2003; Zbl 1031.60015); L. Jiang and Z. Chen, Chin. Ann. Math., Ser. B 25, No. 3, 401–412 (2004; Zbl 1062.60057)].


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60E15 Inequalities; stochastic orderings
Full Text: DOI


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