On Jensen's inequality for g-expectation

被引：18
|
作者：
Jiang, L [1 ]
Chen, ZJ
机构：
[1] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Peoples R China
[2] China Univ Min & Technol, Dept Math, Jiangsu 221008, Peoples R China
[3] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Peoples R China
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2004年 / 25卷 / 03期
关键词：
backward stochastic differential equation; Jensen's inequality; g-expectation; comparison theorem;
D O I：
10.1142/S0252959904000378
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Briand et al. gave a counterexample showing that given g, Jensen's inequality for g-expectation usually does not hold in general. This paper proves that Jensen's inequality for g-expectation holds in general if and only if the generator g(t, z) is super-homogeneous in z. In particular, g is not necessarily convex in z.
引用
收藏
页码：401 / 412
页数：12
相关论文
共 50 条
  • [31] Martingale Inequalities under G-Expectation and Their Applications
    Li, Hanwu
    ACTA MATHEMATICA SCIENTIA, 2021, 41 (02) : 349 - 360
  • [32] Supermartingale decomposition theorem under G-expectation
    Li, Hanwu
    Peng, Shige
    Song, Yongsheng
    ELECTRONIC JOURNAL OF PROBABILITY, 2018, 23
  • [33] Jensen's Inequality Under Nonlinear Expectation Generated by BSDE with Jumps
    Na ZHANG
    Guang-yan JIA
    Acta Mathematicae Applicatae Sinica, 2019, 35 (04) : 873 - 884
  • [34] Jensen's Inequality Under Nonlinear Expectation Generated by BSDE with Jumps
    Zhang, Na
    Jia, Guang-yan
    ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2019, 35 (04): : 873 - 884
  • [35] A result on the probability measures dominated by g-expectation
    Jiang L.
    Chen Z.-J.
    Acta Mathematicae Applicatae Sinica, 2004, 20 (3) : 507 - 512
  • [36] Jensen’s Inequality Under Nonlinear Expectation Generated by BSDE with Jumps
    Na Zhang
    Guang-yan Jia
    Acta Mathematicae Applicatae Sinica, English Series, 2019, 35 : 873 - 884
  • [37] MARTINGALE INEQUALITIES UNDER G-EXPECTATION AND THEIR APPLICATIONS
    李邯武
    ActaMathematicaScientia, 2021, 41 (02) : 349 - 360
  • [38] A Sufficient and Necessary Condition for G-expectation to be Linear
    Zhang, Qixia
    Sun, Qiliang
    PROCEEDINGS OF THE 2016 INTERNATIONAL CONFERENCE ON EDUCATION, MANAGEMENT AND COMPUTER SCIENCE (ICEMC 2016), 2016, 129 : 374 - 378
  • [39] g-Expectation for Conformable Backward Stochastic Differential Equations
    Luo, Mei
    Feckan, Michal
    Wang, Jin-Rong
    O'Regan, Donal
    AXIOMS, 2022, 11 (02)
  • [40] Optimal Multiple Stopping Problems Under g-expectation
    Hanwu Li
    Applied Mathematics & Optimization, 2022, 85
12345