A real valued function h defined on R is called g-convex if it satisfies the "generalized Jensen's inequality" for a given g-holds for all random variables X such that both sides of the inequality are meaningful. In this paper we will give a necessary and sufficient condition for a C 2 -function being g-convex, and study some more general situations. We also study g-concave and g-affine functions, and a relation between g-convexity and backward stochastic viability property.
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