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G-期望框架下G-凸函数的性质 被引量：1

Properties of G-convex function under the framework of G-expectations
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摘要 证明了在G-期望框架下,函数是G-凸函数等价于函数是经典的凸函数。给出了G-期望的Jensen不等式在G-期望估值方面的应用。 It is proved that, under the framework of G-expectations, a G-convex function is equivalent to a classical convex function. Applications of Jensen＇ s inequalities for G-expectations in numerical estimate are given.
作者 王伟
机构地区 山东大学数学学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2009年第4期43-46,共4页 Journal of Shandong University(Natural Science)
基金 国家重点基础研究发展计划(973)资助项目(2007CB814901)
关键词 G-期望 G-凸函数 JENSEN不等式 G-expectation G-convex function Jensen＇s inequality
分类号 O211.6 [理学—概率论与数理统计]
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参考文献8

  • 1CHEN Zengjing, KULPERGER R, JIANG Long. Jensen's inequality for g-expectation, part 1[J]. C R Acad Sci Paris Ser I, 2003, 337 : 725-730.
  • 2CHEN Zengjing, KULPERGER R, JIANG Long. Jensen's inequality for g-expectation: part 2[J]. C R Acad Sci Paris Ser I, 2003, 337 : 797-800.
  • 3JIANG 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..ON JENSEN'S INEQUALITY FOR g-EXPECTATION[J].Chinese Annals of Mathematics,Series B,2004,25(3):401-412. 被引量：26
  • 4HU Ying. On Jensen's inequality for g-expectation and for nonlinear expectation[J]. Archiv der Mathematik, 2005, 85:572-580.
  • 5JIA Guangyan, PENG Shige. Jensen' s inequality for g-convex fuction under g-expectation[EB/OL]. (2008-00-04)[2008-08-15]. http://arxiv.org/abs/0800. 0373.
  • 6PENG Shige. G-Expectation, G-Brownian motion and related stochastic calculus of Ito's type[C]// BENTH F E, NUNNO G D, LINDSTRΦM T, et al. Stochastic Analysis and Applications. Berlin, Heidelberg: Springer-verlag, 2007: 541-567.
  • 7PENG Shige. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation[J]. Stochastic Processes and Applications, 2008, 12 (118) : 2223-2253.
  • 8PENG Shige.NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS[J].Chinese Annals of Mathematics,Series B,2005,26(2):159-184. 被引量：29

二级参考文献52

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共引文献53

同被引文献7

  • 1JIANG 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..ON JENSEN'S INEQUALITY FOR g-EXPECTATION[J].Chinese Annals of Mathematics,Series B,2004,25(3):401-412. 被引量：26
  • 2PENG Shige. BSDE and related g-expectations [M ]//E1 KAROUI, MAZLIAK L. Pitman Research Notes in Mathematics Se- ries(364) : Backward Stochastic Differential Equations. Harlow: Addison Walsey Longman, 1997: 141-159.
  • 3CHEN Zengjing, KULPERGER R, JIANG Long. Jensen's inequality for g-expectation, part I [J]. C R Acad Sci Paris S6r I , 2003, 337:725-730.
  • 4CHEN Zengjing, KULPERGER R, JIANG Long. Jensen's inequality for g-expectation, part 1I [J]. C R Acad Sci Paris S6r I , 2003, 337:797-800.
  • 5PENG Shige. G-expectation, G-Brownian motion and related stochastic calculus of It6's type [ C ]// The Abel Symposium 2005 on Stochastic Analysis and Applications. New York: Springer-Verlag, 2006: 541-567.
  • 6PENG Shige. A new central limit theorem under sublinear expectations [ EB/OL ]. [ 2008-03-18 ] [2010-04-16 ]. http :// arX- iv: 0803. 2656vl Emath. PR].
  • 7PENG Shige. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation[ J ]. Stochastic Processes and Applications, 2008, 118 (12) :2223-2253.

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山东大学学报（理学版）
2009年 第4期

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