数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (2): 349-360.doi: 10.1007/s10473-021-0201-6

• 论文 •    下一篇

MARTINGALE INEQUALITIES UNDER G-EXPECTATION AND THEIR APPLICATIONS

李邯武   

  1. Center for Mathematical Economics, Bielefeld University, Bielefeld 33615, Germany
  • 收稿日期:2019-01-31 修回日期:2019-12-11 出版日期:2021-04-25 发布日期:2021-04-29
  • 作者简介:Hanwu LI,E-mail:hanwu.li@uni-bielefeld.de,lihanwu11@163.com
  • 基金资助:
    The author is supported by the German Research Foundation (DFG) via CRC 1283.

MARTINGALE INEQUALITIES UNDER G-EXPECTATION AND THEIR APPLICATIONS

Hanwu LI   

  1. Center for Mathematical Economics, Bielefeld University, Bielefeld 33615, Germany
  • Received:2019-01-31 Revised:2019-12-11 Online:2021-04-25 Published:2021-04-29
  • About author:Hanwu LI,E-mail:hanwu.li@uni-bielefeld.de,lihanwu11@163.com
  • Supported by:
    The author is supported by the German Research Foundation (DFG) via CRC 1283.

摘要: In this paper, we study the martingale inequalities under $G$-expectation and their applications. To this end, we introduce a new kind of random time, called $G$-stopping time, and then investigate the properties of a $G$-martingale (supermartingale) such as the optional sampling theorem and upcrossing inequalities. With the help of these properties, we can show the martingale convergence property under $G$-expectation.

关键词: $G$-expectation, $G$-supermartingale, upcrossing inequality

Abstract: In this paper, we study the martingale inequalities under $G$-expectation and their applications. To this end, we introduce a new kind of random time, called $G$-stopping time, and then investigate the properties of a $G$-martingale (supermartingale) such as the optional sampling theorem and upcrossing inequalities. With the help of these properties, we can show the martingale convergence property under $G$-expectation.

Key words: $G$-expectation, $G$-supermartingale, upcrossing inequality

中图分类号: 

  • 60G42