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A note on Jensen’s inequality for BSDEs
Authors:Sheng Jun Fan
Institution:College of Sciences, China University of Mining ~z Technology, Xuzhou 221008, P. R. China
Abstract:Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen’s inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g(t, 0) = 0, a.s., a.e.. In this paper, based on Jiang’s results, under the same assumptions as Jiang’s, we investigate the necessary and sufficient condition on g under which Jensen’s inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen’s inequality for BSDEs.
Keywords:backward stochastic differential equation  Jensen's inequality  g-expectation  Jensen's inequality for BSDEs
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