The minimal sublinear expectations and their related properties

In this paper, we prove that for a sublinear expectation E[·] defined on L2(Ω, F, P ), the following statements are equivalent: (i) E is a minimal member of the set of all sublinear expectations defined on L2(Ω, F, P ); (ii) E is linear; (iii) the two-dimensional Jensen's inequality for E holds. Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.