Fτ-Coherent 风险度量

数学物理学报

F_τ-Coherent 风险度量

陈文财; 叶中行

上海交通大学数学系上海 200240

收稿日期:2005-04-13 修回日期:2006-12-21 出版日期:2007-10-25 发布日期:2007-10-25
通讯作者: 陈文财
基金资助:
国家自然科学基金(10171066和70671069)和上海市基础研究重点项目(02DJ14063)资助

F_τ-Coherent Risk Measures

Chen Wencai ; Ye Zhongxing

Mathematics Department of Shanghai Jiaotong University, Shanghai 200240

Received:2005-04-13 Revised:2006-12-21 Online:2007-10-25 Published:2007-10-25
Contact: Chen Wencai

摘要/Abstract

摘要：

该文提出了一个风险度量的新概念,即定义在任意停时 τ上的 F_τ-Coherent 风险度量. 对任一满足Fatou 性质的F_τ-Coherent 风险调整值度量(即一个F_τCoherent风险度量的负值) ф_т: L^∞ (F) →L^∞ (F_τ) 我们都可以用一个 F_τ-凸概率测度集来给出它的显式表示.同时我们还证明了一个 F_τ-Coherent 风险调整值度量可以用它的可接受头寸集合来表示.

关键词: 风险度量, F_τ-Coherent, 表示定理, - F_τ-凸集, 可接受头寸集合

Abstract: The authors present in this paper a new concept of risk measure defined at an arbitrary stopping time τ, the F_τ-coherent risk measure. For an F_τ-coherent risk adjusted value (the negative of a F_τ-coherent risk measure) ф_т: L^∞ (F) →L^∞ (F_τ), which satisfies the Fatou property, its representation theorem is obtained by using a special F_τ-convex set of probability measures. It is also proven that an F_τ-coherent risk adjusted value can be represented by its acceptance set.

Key words:
Risk measure, F_τ-coherent, Representation theorem, F_τ-covex, Acceptance set.

中图分类号:

91B30

陈文财; 叶中行. F_τ-Coherent 风险度量[J]. 数学物理学报, 2007, 27(5): 830-838.

Chen Wencai ; Ye Zhongxing. F_τ-Coherent Risk Measures[J]. Acta mathematica scientia,Series A, 2007, 27(5): 830-838.

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