一种新的风险度量方法-GVaR  

A New Risk Measure Method-GVaR

作　　者：苑慧玲 穆燕 周勇[2,1] YUAN HULLING;MU YAN;ZHOU YONG(Department of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China;Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China)

机构地区：[1]上海财经大学统计与管理学院,上海200433 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《应用数学学报》2017年第6期883-893,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金委重点项目(71331006);国家自然科学重大研究计划重点项目(91546202);中国科学院重点实验室(2008DP173182);国家数学与交叉科学中心(2008DP173182);上海财经大学创新团队支持计划(IRTSHUFE13122402);上海财经大学研究生创新基金(CXJJ-2015-443)资助

摘　　要：探讨科学的风险度量方法一直是风险管理中的重要课题.本文在G-期望和G-正态分布理论的基础上,研究了某一类金融资产的风险不确定性问题.首先针对不确定环境下的金融市场,提出了损失函数为f(y)=y的一种新的GVaR风险度量方法,从而改进了传统的VaR方法,建立并证明了GVaR是一致性风险度量的定理,并且在特殊情形下给出了GVaR值的函数表达式,便于在实际中应用·本文利用GVaR方法从一个新的角度解释风险度量,正如我们所坚信地,GVaR度量在风险管理中是一个全新的精确的风险度量方法和技术.希望这个新的度量方法GVaR能够为金融学者,银行,投资部门以及相关的决策者提供建议.It has been an important topic to explore the scientific risk measure method in risk management. On the basis of G-expectation and G-normal distribution theory, the uncertain problem of some financial asset risks are studied in this paper. GVaR risk measurement method is proposed when the loss function of a financial asset is given as f（y） = y. The new risk measurement GVaR extents the traditional VaR method, and is a coherent risk measurement via the theroem. In special cases, we can obtain a closed form for the GVaR measurement, which is convenient to be applied in practice. In this paper, GVaR method is used to explain the risk measurement in a new perspective, as we believe, GVaR measurement is a new accurately risk measure method and technology in risk management. We also hope that the new measure method GVaR could provide some suggestion for financial scholars, the banks, the investment departments and the relative policy makers.

关 键 词：G正态分布 G期望 损失函数 GVaR 

分 类 号：O212[理学—概率论与数理统计] F830[理学—数学]