中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (5): 153-158.doi: 10.13471/j.cnki.acta.snus.2019.05.019

• 论文 • 上一篇    

次线性g-期望的性质及其应用

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:2019-04-10 出版日期:2019-09-25 发布日期:2019-09-25
  • 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

Properties of sublinear g-expectations and their applications

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:2019-04-10 Online:2019-09-25 Published:2019-09-25

摘要:

在倒向随机微分方程生成元满足基本假设的前提下,证明了g-期望的次可加性与生成元函数之间的对应关系,获得了g-期望的正齐次性与生成元函数之间的对应关系, 从而在g-期望的框架下说明了Detlefsen-Scandolo (2005)与Jiang (2008)中关于动态一致性风险度量的两种定义方式是完全一致的。进一步地,获得了一类时间相容的动态一致性风险度量与g-期望的次线性性之间的对应关系。

关键词: 倒向随机微分方程, 次线性g期望, 动态一致性风险度量

Abstract:

Under the basic assumptions on generators of backward stochastic differential equations, the one-to-one correspondence between subadditivity (resp. homogeneity) of g-expectations and generators of backward stochastic differential equations is obtained. Thus it is proved that the definitions of dynamic coherent risk measures in Detlefsen-Scandolo (2005) and Jiang (2008) are completely same under the framework of g-expectations. Furthermore, the relationship between time-consistent dynamic coherent risk measures via g-expectations and sublinearity of g-expectations is established.

Key words: backward stochastic differential equation, sublinear gexpectation, dynamic coherent risk measure

中图分类号: