| ON JENSEN’S INEQUALITY FOR g-EXPECTATION |
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| 作者姓名： | JIANG Long CHEN Zengjing |
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| 作者单位： | 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. |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No.10131030) |
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| 摘 要： | Briand et al. gave a counterexample showing that given g, Jensen's inequalityfor g-expectation usually does not hold in general. This paper proves that Jensen'sinequality for g-expectation holds in general if and only if the generator g(t,z) issuper-homogeneous in z. In particular, g is not necessarily convex in z.
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| 关 键 词： | Backward stochastic differential equation Jensen’s inequality g-expectation Conditional g-expectation Comparison theorem |
| 收稿时间： | 3/3/2004 12:00:00 AM |
| 修稿时间： | 2009/11/3 0:00:00 |
ON JENSEN'S INEQUALITY FOR g-EXPECTATION |
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| JIANG Long,CHEN Zengjing.ON JENSEN''''S INEQUALITY FOR g-EXPECTATION[J].Chinese Annals of Mathematics,Series B,2004,25(3):401-412. |
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| Authors: | JIANG Long and CHEN Zengjing |
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| Institution: | 1. School of Mathematics and System Sciences, Shandong University, Jinan 250100, China;Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China
2. School of Mathematics and System Sciences, Shandong University, Jinan 250100, China |
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| Abstract: | 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. |
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| Keywords: | Backward stochastic differential equation Jensen's inequality g-expectaation Conditional g-expectation Comparison theorem |
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