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

页码：401 / 412

页数：12

共 50 条

[1] ON JENSEN'S INEQUALITY FOR g-EXPECTATION
JIANG LONG
CHEN ZENGJING School of Mathematics and System Sciences
Chinese Annals of Mathematics,Series B, 2004, (03) : 401 - 412
[2] On Jensen’s inequality for g-expectation and for nonlinear expectation
Ying Hu
Archiv der Mathematik, 2005, 85 : 572 - 580
[3] On Jensen's inequality for g-expectation and for nonlinear expectation
Ying, H
ARCHIV DER MATHEMATIK, 2005, 85 (06) : 572 - 580
[4] On Jensen's inequality and Holder's inequality for g-expectation
Jia, Guangyan
ARCHIV DER MATHEMATIK, 2010, 94 (05) : 489 - 499
[5] Jensen's inequality for g-expectation:: part 1
Chen, ZJ
Kulperger, R
Jiang, L
COMPTES RENDUS MATHEMATIQUE, 2003, 337 (11) : 725 - 730
[6] Jensen's inequality for g-expectation, Part 2
Chen, ZJ
Kulperger, R
Jiang, L
COMPTES RENDUS MATHEMATIQUE, 2003, 337 (12) : 797 - 800
[7] On Jensen’s inequality and Hölder’s inequality for g-expectation
Guangyan Jia
Archiv der Mathematik, 2010, 94 : 489 - 499
[8] Jensen's inequality for g-convex function under g-expectation
Jia, Guangyan
Peng, Shige
PROBABILITY THEORY AND RELATED FIELDS, 2010, 147 (1-2) : 217 - 239
[9] Jensen's inequality for g-expectation with non-Lipsehitz generator
School of Sciences, China University of Mining and Technology, Xuzhou 221116, China
Zhongguo Kuangye Daxue Xuebao, 2008, 1 (142-146):
[10] Jensen’s inequality for g-convex function under g-expectation
Guangyan Jia
Shige Peng
Probability Theory and Related Fields, 2010, 147 : 217 - 239

← 1 2 3 4 5 →