风险度量与风险管理的新工具ES  

Expected shortfall( ES) : a new tool for risk measure and risk management

作　　者：陈文财[1] 齐肖阳 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（工科版）》2014年第2期195-199,共5页Journal of Nanchang University(Engineering & Technology)

基　　金：江西省教育厅科技资助项目(GJJ14157)

摘　　要：采用资产组合损失变量描述风险,并基于损失分布的α-(上)分位数给出"期望巨额损失值"ES(expected shortfall)和"条件风险价值"CVaR(conditional value at risk)的定义。在一般损失分布下,通过直接计算说明了任一资产组合损失变量的"期望巨额损失值"ES的定义与α-(上)分位数的选取无关;而且也通过直接计算证明了ES与CVaR两者的等价关系;进而通过构造出ES的概率测度族表示证明了ES是一致性风险度量方法。此外,还就相关问题,例如分位数、一致性风险度量、尾部条件期望TCE等,给出了一些有价值的注记。Based on loss variables describing corresponding financial portfolios＇ risk and α-quantile （upper tail） of loss distribution,the definitions of expected shortfall （ES） and conditional value at risk （CVaR） were set up. Under general loss distributions,it has been proved by some direct calculations that the definition of ES was independent on the choice of α-quantile for any loss variable;also by some direct calculations the equivalence between ES and CVaR has been checked ; and furthermore by constructing a set of probability measures with which ES could be represented for any loss variable, the coherence of ES as a risk measure has been discovered. More over, there were some important remarks in this paper for some correlated topics, e. g. , α-quantile, coherent risk measure, tail conditional expectation （ TCE）, etc.

关 键 词：期望巨额损失值 条件风险价值 α-分位数 尾部条件期望 一致性风险度量 

分 类 号：O211.9[理学—概率论与数理统计] F064.1[理学—数学]