广西师范大学学报（自然科学版） ›› 2016, Vol. 34 ›› Issue (4): 38-45.doi: 10.16088/j.issn.1001-6600.2016.04.006

• 广西高校优秀中青年骨干教师培养工程论坛 • 上一篇    下一篇

VaR和ES的贝叶斯经验似然估计

张军舰,赖廷煜,杨晓伟   

  1. 广西师范大学数学与统计学院,广西桂林541004
  • 收稿日期:2016-07-08 出版日期:2016-07-18 发布日期:2018-07-18
  • 通讯作者: 张军舰(1973—),男,河南内乡人,广西师范大学教授,博士。E-mail:jjzhang@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11261009);广西自然科学基金资助项目(2012GXNSFAA053004);广西高等学校优秀中青年骨干教师培养工程资助项目;广西师范大学研究生创新基金资助项目(Ycsw2013058)

Bayesian Empirical Likelihood Estimation on VaR and ES

ZHANG Junjian, LAI Tingyu, YANG Xiaowei   

  1. College of Mathematics and Statistics, Guangxi Normal University,Guilin Guangxi 541004, China
  • Received:2016-07-08 Online:2016-07-18 Published:2018-07-18

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摘要： 风险价值(VaR)和预期亏损(ES)能较好地度量金融投资组合的最大损失,研究其估计具有重大意义。本文利用贝叶斯经验似然方法对VaR和ES进行估计,理论上讨论了该估计的相合性和渐近正态性。模拟结果显示,在合适的先验信息下,本文所提出的估计具有一定的优势,有较好的应用前景。

关键词: 风险价值, 预期亏损, 贝叶斯经验似然

Abstract: VaR(value at risk) and ES(expected shortfall) are used to measure the loss of financial investment. It is interesting to investigate the estimation of VaR and ES. In this paper, VaR and ES are estimated by Baysian empirical likelihood method. Some properties,such as consistence and asymptotic normality,are given. Simulation studies show that,with some prior information,Baysian empirical likelihood is a better method.

Key words: value at risk, expected shortfall, Bayesian empirical likelihood

中图分类号: 

  • O212.1
[1] JORIAN P. Risk2: Measuring the risk in Value at Risk[J]. Financial Analysis Journal, 1996, 52(6):47-56. DOI:10.2469/faj.v52.n6.2039.
[2] ARTZNER P, DELBAEN F, EBER J M, et al. Thinking coherently[J]. Risk, 1997, 10: 68-71.
[3] ARTZNER P, DELBAEN F, EBER J M, et al. Coherent measures of risk[J]. Mathematical Finance, 1999, 9(3):203-228. DOI:10.1111/1467-9965.00068.
[4] ROCKAFELLAR R T, URYASEV S. Conditional Value-at-Risk for general loss distributions[J]. Journal of Banking and Finance, 2002, 26(7): 1443-1471. DOI:10.1016/S0378-4266(02)00271-6.
[5] PFLUG G C. Some remarks on the Value-at-Risk and the conditional Value-at-Risk[M]// URYASEV S. Probabilistic Constrained Optimization: Methodology and Applications. Dordrecht: Kluwer Academic Publisher, 2000: 272-281. DOI:10.1007/978-1-4757-3150-7_15.
[6] ACERBI C, TASCHE D. Expected shortfall: A natural coherent alternative to value at risk[J]. Economic Notes, 2002, 31(2):379-388. DOI:10.1111/1468-0300.00091.
[7] ACERBI C, TASCHE D. On the coherence of expected shortfall[J]. Journal of Banking and Finance, 2002, 26(7):1487-1503. DOI:10.1016/S0378-4266(02)00283-2.
[8] 晏振. VaR和ES的调整经验似然估计[D]. 桂林: 广西师范大学, 2012.
[9] OWEN A B. Empirical likelihood ratio confidence intervals for a single functional[J]. Biometrika, 1988,75(2): 237-249. DOI:10.1093/biomet/75.2.237.
[10] OWEN A B. Empirical likelihood[M]. London: Chapman and hall, 2001.
[11] QIN Jin, LAWLESS J. Empirical likelihood and general eatimating equations[J]. Annals of Statistics, 1994,22(1):300-325. DOI:10.1214/aos/1176325370.
[12] 张新成,张军舰,詹欢. 基于垂直密度表示的经验欧氏拟合优度检验[J]. 广西师范大学学报(自然科学版),2013,31(4):60-65. DOI:10.16088/j.issn.1001-6600.2013.04.001.
[13] LAZAR N A. Bayesian empirical likelihood[J]. Biometrika, 2003, 90(2): 319-326. DOI:10.1093/biomet/90.2.319.
[14] YANG Yunwen, HE Xuming. Bayeian empirical likelihood for quantile regression[J]. The Annals of Statistics, 2012, 40(2):1102-1131. DOI:10.1214/12-AOS1005.
[15] RAO J N K, WU Changbao. Bayesian pseudo-empirical-likelihood intervals for complex surveys[J]. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2010, 72(4):533-544. DOI:10.1111/j.1467-9868.2010.00747.x.
[16] Van der VAART A W. Asymptotic statistics[M]. Cambridge: Cambridge University Press, 1998.
[17] MOLANES-L PEZ E M, Van KEILEGOM I, VERAVERBEKE N. Epirical likelihood for non-smooth criterion functions[J]. Scandinavian Journal of Statistics, 2009, 36(3):413-432. DOI:10.1111/j.1467-9469.2009.00640.x.
[18] HE Xuming, SHAO Qiman. A general Bahadur representation of M-estimators and its application to linear regression with nonstochastic designs[J]. The Annals of Statistics, 1996, 24(6):2608-2630. DOI:10.1214/aos/1032181172.
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