二次交替容度的AVaR的表示定理

华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (3): 23-29.

二次交替容度的AVaR的表示定理

田德建, 江龙, 纪荣林

中国矿业大学~~理学院, 徐州 221116

收稿日期:2013-05-01 修回日期:2013-08-01 出版日期:2014-05-25 发布日期:2014-07-25

Representation theorem for AVaR under a submodular capacity

TIAN De-jian, JIANG Long, JI Rong-lin

School of Sciences, China University of Mining and Technology, Xuzhou 221116, China

Received:2013-05-01 Revised:2013-08-01 Online:2014-05-25 Published:2014-07-25

摘要/Abstract

摘要： 从分位数函数的角度出发,
首先定义了金融头寸在容度空间下的\,VaR\,和\,AVaR.
然后综合运用\,Choquet\,积分的性质以及概率测度空间下\,AVaR\,的结果,
建立了基于二次交替容度的\,AVaR\,的表示定理.
进一步得到了基于二次交替容度的\,AVaR\,为一致性风险度量,
推广了经典的结果.

关键词: AVaR, 分位数函数, 表示定理, 二次交替容度

Abstract: From the viewpoints of quantile functions, we gave the
definition of AVaR of financial positions under a capacity. Then,
using the classical results of AVaR under the probability measure,
we established the representation theorem for AVaR under the
submodular capacity. As a byproduct of this representation theorem,
we proved that AVaR under a submodular capacity is a coherent risk
measure, which generalized the classical results.

Key words: AVaR, quantile function, representation theorem, submodular capacity

中图分类号:

O211

田德建, 江龙, 纪荣林. 二次交替容度的AVaR的表示定理[J]. 华东师范大学学报(自然科学版), 2014, 2014(3): 23-29.

TIAN De-jian, JIANG Long, JI Rong-lin. Representation theorem for AVaR under a submodular capacity[J]. Journal of East China Normal University(Natural Sc, 2014, 2014(3): 23-29.