中山大学学报(自然科学版) ›› 2020, Vol. 59 ›› Issue (4): 144-148.doi: 10.13471/j.cnki.acta.snus.2019.06.25.2019A050

• • 上一篇    下一篇

非线性数学期望的一些性质研究

黄安琪1,2, 周津名3, 纪荣林2   

  1. 1. 对外经济贸易大学国际经济贸易学院,北京 100029
    2. 安徽大学数学科学学院,安徽 合肥 230601
    3. 合肥师范学院数学与统计学院,安徽 合肥 230601
  • 收稿日期:2019-06-25 出版日期:2020-07-25 发布日期:2020-07-25
  • 通讯作者: 纪荣林(1984年生),男;研究方向:金融数学;E-mail:jironglin@ahu.edu.cn
  • 作者简介:黄安琪(1998年生),女;研究方向:金融数学;E-mail:ahuhuangaq@163.com

Some properties of nonlinear expectations

HUANG Anqi1,2ZHOU Jinming3JI Ronglin2   

  1. 1. School of International Trade and EconomicsUniversity of International Business and EconomicsBeijing 100029China
    2. School of Mathematical SciencesAnhui UniversityHefei 230601China
    3. School of Mathematics and StatisticsHefei Normal UniversityHefei 230601China
  • Received:2019-06-25 Online:2020-07-25 Published:2020-07-25

摘要: 在公理化假设的基本框架下,建立了次线性期望 (超线性期望) 与一致性风险度量之间的对应关系。
进一步地,在对非线性数学期望附加一定的连续性假设的条件下,建立了凸期望 (凹期望) 与凸风险度量之间
的内在联系。

关键词: 非线性数学期望, 次线性期望, 凸期望, 一致性风险度量, 凸风险度量

Abstract: Under the axiomatic assumptions for nonlinear expectations and financial risk measuresthe relation between sublinear expectations (Resp. superlinear expectations) and coherent risk measures is obtained, respectively. Furthermore, under a natural continuous assumption for the nonlinear expectations, the relationship between convex expectations (Resp. concave expectations) and convex risk measures is also established, respectively.

Key words: nonlinear expectation, , sublinear expectation, , convex expectation, , coherent risk measure, , convex risk measure

中图分类号: