On the minimal members of convex expectations

Abstract In this paper, we show that for a convex expectation E [ ⋅ ] defined on L 1 ( Ω , F , P ) , the following statements are equivalent: (i) E is a minimal member of the set of all convex expectations defined on L 1 ( Ω , F , P ) ; (ii) E is linear; (iii) two-dimensional Jensen inequality for E holds. In addition, we prove a sandwich theorem for convex expectation and concave expectation.