Jensen's inequality for g-expectation:: part 1

Briand et al. (Electron. Comm. Probab. 5 (2000) 101-117) gave a counterexample and proposition to show that given g, g-expectations usually do not satisfy Jensen's inequality for most of convex functions. This yields a natural question, under which conditions on g, do g-expectations satisfy Jensen's inequality for convex functions? In this paper, we shall deal with this question in the case that g is convex and give a necessary and sufficient condition on g under which Jensen's inequality holds for convex functions. (C) 2003 Academie des sciences. Published by Elsevier SAS. All rights reserved.