随机极限正态分布下的GCVaR风险度量研究
Study on Risk Measure of GCVaR under Random Limit Normal Distribution

DOI: 10.12677/SA.2019.83050, PP. 456-462

Keywords: 非线性期望，随机正态分布，一致性风险度量
Nonlinear Expectation, Random Limit Normal Distribution, Coherent Risk Measure

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文阐明经典的概率统计理论和方法，在不确定性金融风险度量领域的不完全适用性及相应风险度量模型不确定性存在的根源。进而在非线性期望理论基础上，通过构建随机极限正态分布G-正态分布，结合VaR、CVaR风险度量模型，定义了随机极限风险度量模型GVaR和GCVaR。最后，理论上证明了以上两种风险度量模型是合理的、恰当的一致性风险度量。
This paper first illustrates classical probability statistics theory and method, the incomplete applicability in the field of uncertainty financial risk measurement, and the origin of the uncertainty of the coherent risk measurement model. Then, based on the nonlinear expectation theory, by constructing the G-normal distribution of the random limit normal distribution, combining the VaR and CVaR risk measurement model, we define the random limit risk measurement model GVaR and GCVaR. Finally, the above two risk measurement models are proved to be reasonable and appropriate coherent risk measurements.

References

[1]	宫晓琳, 杨淑振. 非线性期望理论与基于模型不确定性的风险度量[J]. 经济研究, 2015 ,11(1): 133-147.
[2]	Peng, S.G. (2006) G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito’s Type. Stochastic Analysis & Applications, 1, 3-25.
[3]	Peng, S.G. (2007) G-Brownian Motion and Dynamic Risk Measure under Volatility Uncentainly. Princeton: Princeton University Press.
[4]	王鹏. G-期望及其相关计算问题[D]: [硕士学位论文]. 上海: 上海交通大学, 2011.
[5]	Artzner, P., Delban Eber, J.M. and Heath, D. (1999) Coherent measures of risk. Mathematical Finance, 4, 203-222. https://doi.org/10.1111/1467-9965.00068
[6]	Rockafellar, R.T. and Uryasev, S. (2000) Optimization of Condi-tional Value-at-Risk. Journal of Risk, 2, 493-517. https://doi.org/10.21314/JOR.2000.038
[7]	宋光辉, 吴超. 互联网金融风险度量模型选择研究[J]. 金融理论与实践, 2014, 12(1)：16-19.
[8]	Morgan, J.P. (1996) Riskmetrics-Technical Document. Morgan Mearant Trust Company, New York, 133-167.
[9]	王伟. 非线性数学期望及其在金融中的应用[D]: [博士学位论文]. 济南: 山东大学, 2006.

Full-Text