中山大学学报自然科学版 ›› 2017, Vol. 56 ›› Issue (6): 72-75.

• 论文 • 上一篇    下一篇

关于凸期望的极小元的一些结果

纪荣林1,周津名2   

  1. 1. 安徽大学数学科学学院,安徽 合肥 230601;
    2. 合肥师范学院数学与统计学院,安徽 合肥 230601
  • 收稿日期:2017-02-08 出版日期:2017-11-25 发布日期:2017-11-25
  • 通讯作者: 周津名(1982年生),女;研究方向:非线性数学期望;E-mail: zjminguv@163.com

Some results on the minimal members of convex expectations

JI Ronglin1,ZHOU Jinming2   

  1. 1. School of Mathematical Sciences, Anhui University, Hefei 230601, China;
    2. School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, China
  • Received:2017-02-08 Online:2017-11-25 Published:2017-11-25

摘要:

在非线性数学期望的公理化框架下,从凸期望和凹期望之间的Sandwich定理的视角出发,研究了带控制条件的凸期望集合的极小元问题,建立了一类带单边或双边控制条件的凸期望集合的极小元的论断与Sandwich定理之间的等价关系。

关键词: 非线性数学期望, 凸期望, Sandwich定理, 极小元

Abstract:

Under the framework of nonlinear expectations,the minimal members of convex expectations with some dominating conditions are studied in the view of the Sandwich theorem for a convex expectation and a concave expectation. The conclusions of the minimal members of convex expectations with single or two dominating conditions are proved to be equivalent to the Sandwich theorem.

Key words: nonlinear expectation, convex expectation, Sandwich theorem, minimal member

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