ON JENSEN'S INEQUALITY FOR g-EXPECTATION
被引量：26
ON JENSEN'S INEQUALITY FOR g-EXPECTATION
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.
作者
JIANG LONG
CHEN ZENGJING School of Mathematics and System Sciences, Shandong University, Jinan 250100, China. Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu,China. E-mail: jianglong@math.sdu.edu.cn School of Mathematics and System Sciences, Shandong University, Jinan 250100, China.
基金
Project supported by the National Natural Science Foundation of China (No.10131030)
参考文献8
-
1[1]Peng, S., BSDE and related g-expectations, Pitman Research Notes in Mathematics Series, 364, 1997,141-159.
-
2[2]Chen, Z. & Epstein, L., Ambiguity, risk and asset returns in continuous time, Econometrica, 70(2002),1403-1443.
-
3[3]Briand, P., Coquet, F., Hu, Y., Memin, J. & Peng, S., A converse comparison theorem for BSDEs and related properties of g-expectation, Electon. Comm. Probab., 5(2000), 101-117.
-
4[4]Coquet, F., Hu, Y., Memin, J. & Peng, S., Filtration consistent nonlinear expectations and related g-expectation, Probab. Theory Related Fields, 123(2002), 1-27.
-
5[5]Chen, Z. & Peng, S., A general downcrossing inequality for g-martingales, Statistics and Probability Letters, 46(2000), 169-175.
-
6[6]Pardoux, E. & Peng, S., Adapted solution of a backward stochastic differential equation, Systems Control Letters, 14(1990), 55-61.
-
7[7]Peng, S., A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation,Stochastics, 38:2(1992), 119-134.
-
8[8]El Karoui, N., Peng, S. & Quenez, M. C., Backward stochastic differential equations in finance, Math.Finance, 7:1(1997), 1-71.
同被引文献86
-
1JIANG Long Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China,Institute of Mathematics, Fudan University, Shanghai 200433, China,School of Mathematics and System Sciences, Shandong University, Jinan 250100, China.Limit theorem and uniqueness theorem of backward stochastic differential equations[J].Science China Mathematics,2006,49(10):1353-1362. 被引量：6
-
2JIA GuangYan School of Mathematics, Shandong University, Jinan 250100, China.The minimal sublinear expectations and their related properties[J].Science China Mathematics,2009,52(4):785-793. 被引量：5
-
3WU LiMing1,2, YAO Nian3 & ZHANG ZhengLiang31Laboratoire de Mathématiques Appliquées, CNRS-UMR 6620, Université Blaise Pascal, 63177 Aubière, France,2Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100190, China,3Department of Mathematics, Wuhan University, Wuhan 430072, China.L^1-uniqueness of Sturm-Liouville operators[J].Science China Mathematics,2010,53(1):173-178. 被引量：1
-
4PENG ShiGe Institute of Mathematics,Shandong University,Jinan 250100,China.Survey on normal distributions,central limit theorem,Brownian motion and the related stochastic calculus under sublinear expectations[J].Science China Mathematics,2009,52(7):1391-1411. 被引量：54
-
5MENG QingXin1,2 1 Department of Mathematical Sciences,Huzhou University,Zhejiang 313000,China 2 Institute of Mathematics,Fudan University,Shanghai 200433,China.A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information[J].Science China Mathematics,2009,52(7):1579-1588. 被引量：5
-
6ShigePeng.Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims[J].Acta Mathematicae Applicatae Sinica,2004,20(2):191-214. 被引量：19
-
7朱炳泉,毛存孝.印度与欧亚板块东部碰撞边界——腾冲火山岩的Nd-Sr同位素与微量元素研究[J].地球化学,1983,12(1):1-14. 被引量：40
-
8江龙.关于倒向随机微分方程生成元的逆比较定理(英文)[J].应用数学,2004,17(4):575-582. 被引量：2
-
9江龙.倒向随机微分方程生成元的表示定理及其应用(英文)[J].应用概率统计,2005,21(1):53-60. 被引量：5
-
10范胜君.几乎处处意义下倒向随机微分方程解对终值的连续性[J].徐州师范大学学报（自然科学版）,2005,23(1):27-30. 被引量：3
引证文献26
-
1肖昌浩,王庆飞,周兴志,杨立强,张静.腾冲地热区高温热泉水中稀土元素特征[J].岩石学报,2010,26(6):1938-1944. 被引量：10
-
2白山,江龙,何娇.具有共单调可加性的g-期望的一些性质[J].山东大学学报（理学版）,2005,40(2):42-47. 被引量：2
-
3Long JIANG Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China,School of Mathematical Sciences, Fudan University, Shanghai 200433, China,School of Mathematics and System Sciences, Shandong University, Jinan 250100, China..Jensen's Inequality for Backward Stochastic Differential Equations[J].Chinese Annals of Mathematics,Series B,2006,27(5):553-564. 被引量：10
-
4范胜君.g-期望关于凸(凹)函数的Jensen不等式[J].数学年刊（A辑）,2006,27(5):635-644. 被引量：3
-
5高杰.基于g期望的Minkowski不等式[J].黑龙江科技学院学报,2007,17(2):154-156.
-
6徐玉红,刘玉春,高杰.基于g期望的二元Jensen不等式[J].黑龙江科技学院学报,2007,17(3):224-226. 被引量：2
-
7Sheng Jun FAN.A Relationship Between the Conditional g-Evaluation System and the Generator g and Its Applications[J].Acta Mathematica Sinica,English Series,2007,23(8):1427-1434. 被引量：1
-
8朱红艳,索新丽,焦琳.关于g期望的两个不等式[J].徐州工程学院学报,2007,22(8):16-18.
-
9何娇,江龙,刘坤,高杰,高伟.非Lipschitz条件下基于g-期望的Jensen不等式[J].中国矿业大学学报,2008,37(1):142-146. 被引量：1
-
10范胜君,周圣武.半正定(半负定)二元函数基于g-期望的Jensen不等式[J].数学的实践与认识,2008,38(3):80-89. 被引量：1
二级引证文献35
-
1孙秋霞.g-期望关于多元函数的Jensen不等式的必要条件[J].山东科技大学学报（自然科学版）,2007,26(2):109-111. 被引量：2
-
2何娇,江龙,刘坤,高杰,高伟.非Lipschitz条件下基于g-期望的Jensen不等式[J].中国矿业大学学报,2008,37(1):142-146. 被引量：1
-
3刘洪霞,王向荣,杨丽.基于g-期望的关于二元函数的Jensen不等式的充要条件[J].山东理工大学学报（自然科学版）,2008,22(2):72-75.
-
4Sheng-jun Fan.Moment Inequality and Hlder Inequality for BSDEs[J].Acta Mathematicae Applicatae Sinica,2009,25(1):11-20.
-
5何娇.共单调次可加性的g-期望的一些性质[J].苏州市职业大学学报,2009,20(2):70-73.
-
6Sheng Jun FAN.A Note on Jensen’s Inequality for BSDEs[J].Acta Mathematica Sinica,English Series,2009,25(10):1681-1692. 被引量：1
-
7范胜君.条件g-期望的矩不等式[J].数学年刊（A辑）,2009,30(6):771-776. 被引量：1
-
8朱冬芸,江龙,田德建,冯世强.共单调可加g-估价的一些结果[J].中国矿业大学学报,2010,39(5):790-794.
-
9孙倩怡,杨志,绪玉珍.共单调次可加g-估价与生成元g之间的关系[J].黑龙江科技学院学报,2010,20(6):477-480.
-
10宋丽.次线性期望的Jensen不等式[J].山东大学学报（理学版）,2011,46(3):109-111.
-
1高兹文,楼宇同.Callebaut不等式的改进与新证法[J].华东工学院学报,1991(1):81-83.
-
2刘小琼,刘新乐.Jensen不等式在数学上的应用[J].科教文汇,2008(7):185-185.
-
3Panyu WU.Multiple G-Ito integral in G-expectation space[J].Frontiers of Mathematics in China,2013,8(2):465-476. 被引量：3
-
4陈寅,李磊.综述:一般逻辑程序的证明论语义[J].计算机科学,2004,31(9):152-156. 被引量：1
-
5姜海涛.议论文写作中如何论证[J].初中生优秀作文,2012(5):37-38.
-
6LongJIANG.A Property of g-Expectation[J].Acta Mathematica Sinica,English Series,2004,20(5):769-778. 被引量：2
-
7LongJiang Zeng-jingChen.A Result On the Probability Measures Dominated by g-Expectation[J].Acta Mathematicae Applicatae Sinica,2004,20(3):507-512.
-
8张玉平,王世强.模型论弱力迫的证明论特征[J].北京师范大学学报（自然科学版）,1996,32(1):32-35.
-
9刘英.浅谈议论文中的事例转述[J].科学咨询,2015,0(18):129-129.
-
10HUDi-he.Double Conditional Expectation[J].Wuhan University Journal of Natural Sciences,2004,9(6):851-857. 被引量：3
