| 摘要: |
| 本文研究了由一维Lévy过程驱动的倒向随机微分方程(BSDE)的反比较定理.利用一般g-期望下BSDE的反比较定理的证明方法,推导出了一般f-期望下BSDE的反比较定理,并给出了一般f-期望下Jensen不等式成立的充分必要条件. |
| 关键词: 反比较定理 Lévy过程 Jensen不等式 |
| DOI： |
| 分类号:O211.6 |
| 基金项目:Supported by National Natural Science Foundation of China (11126314); 2013 Basic Research Projects at Zhongnan University of Economics and Law (2013019); the Central Universities Research Program in Zhongnan University of Economics and Law (2014066). |
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| CONVERSE COMPARISON THEOREM FOR BSDE DRIVEN BY LÉVY PROCESS AND JENSEN'S INEQUALITY |
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LI Biao1, XU Jing2, ZHANG Bo3
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1.School of Finance, Zhongnan University of Economics and Law, Wuhan 430073, China;2.School of Econ. and Business Administration, Chongqing University, Chongqing 400030, China;3.School of Statistics, Renmin University of China, Beijing 100872, China
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| Abstract: |
| In this paper, we are devoted to the converse comparison theorem for backward stochastic differential equations (BSDEs, for short) driven by 1-dimensional Lévy processes. With the similar method of the converse comparison theorem under g-expectation, we prove the converse comparison theorem under f-expectation. Moreover, we provide a necessary and sufficient condition for the Jensen's inequality to hold under the f-expectation, the nonlinear expectation defined by BSDEs driven by Lévy processes. |
| Key words: converse comparison theorem Lévy process Jensen's inequality |
