The minimal sublinear expectations and their related properties  

作　　者：JIA GuangYan School of Mathematics, Shandong University, Jinan 250100, China 

出　　处：《Science China Mathematics》2009年第4期785-793,共9页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China (973 Program) (Grant No.2007CB814901) (Financial Risk);National Natural Science Foundation of China (Grant No. 10671111)

摘　　要：In this paper, we prove that for a sublinear expectation ?[·] defined on L 2(Ω, $ \mathcal{F} $ ), the following statements are equivalent: ? is a minimal member of the set of all sublinear expectations defined on L 2(Ω, $ \mathcal{F} $ )? is linearthe two-dimensional Jensen’s inequality for ? holds.Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.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.

关 键 词：G-EXPECTATION Jensen’s inequality linear expectation subadditive expectation sublinear expectation 60H10 

分 类 号：O211.67[理学—概率论与数理统计]