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应用数学学报  2011, Vol. 34 Issue (4): 752-768    DOI:
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金融风险管理中VaR度量的光滑估计效率
刘晓倩1, 周勇1,2
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应用数学研究所, 北京 100190
Efficiency of the Smoothed VaR Estimator in Financial Risk Management
LIU Xiaoqian1, ZHOU Yong1,2
1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433;
2. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190
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摘要 本文研究了金融风险管理理论中风险价值(VaR)的非参数核光滑估计和经验估计的效率问题. 对非独立的时间序列损失/收益样本,在均方误差(MSE)准则的意义下引入“亏量”的概念, 亏量越大表明估计效率越低. 并利用亏量对VaR模型的核光滑估计和基于样本分位数的经验估计进行了比较, 在理论上证明了VaR模型的核光滑估计优于经验估计. 同时, 通过计算机模拟证实了理论获得的结论. 本文还对国内沪深两市上的证券投资基金进行了实证分析, 计算了样本基金的VaR风险度量的经验估计和核光滑估计, 并计算了样本基金基于周收益率和VaR估计的风险调整收益(RAROC)值, 以此对样本基金的业绩做出了有用的评价.  
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关键词&alpha   -混合   亏量   经验估计   核光滑估计   风险价值(VaR)     
Abstract: In this paper, we investigate the efficiency of the kernel smoothed estimator and empirical estimator of Value at Risk (VaR). A deficiency in the sense of the mean square error (MSE) is proposed for observed loss/return sample of time series, the larger is deficiency, lower efficiency the estimator. Our theoretical results and simulation studies have shown that the kernel smoothed VaR estimator is more efficient than the empirical VaR estimator. Furthermore, we make empirical studies to real data of six sample funds from Shanghai securities market and calculate their empirical VaR estimators and kernel smoothed VaR estimators. It also provides an improved performance evaluation for these funds by the values of RAROC of these sample funds based on their weekly returns and VaRs, potentially applied to all funds.  
Key wordsα-mixing   deficiency   empirical estimator   kernel smoothed estimator   value at risk (VaR)   
收稿日期: 2010-10-08;
基金资助:

本文得到国家自然科学基金重点基金(10731010), 国家自然科学基金(70911130018), 国家973项目子项目(2007CB814902)和国家杰出青年基金(70825004), 及上海财经大学``211工程''三期重点学科建设项目和上海市重点学科建设(B803), 上海财经大学研究生科研创新基金(CXJJ-2010-351)资助项目.

引用本文:   
. 金融风险管理中VaR度量的光滑估计效率[J]. 应用数学学报, 2011, 34(4): 752-768.
. Efficiency of the Smoothed VaR Estimator in Financial Risk Management[J]. Acta Mathematicae Applicatae Sinica, 2011, 34(4): 752-768.
 
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