The minimal sublinear expectations and their related properties

In this paper, we prove that for a sublinear expectation epsilon[(.)] defined on L-2(Omega, F, P), the following statements are equivalent: (i) E is a minimal member of the set of all sublinear expectations defined on L-2 (Omega, F, P); (ii) E is linear; (iii) the two-dimensional Jensen's inequality for epsilon holds. Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation. Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.