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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (5): 667-676.doi: 10.3969/j.issn.1005-3085.2015.05.005

• • 上一篇    下一篇

柏拉图-伽玛模型下TVaR风险度量的贝叶斯估计

章  溢1,2,  周东琼3,   温利民1,4   

  1. 1- 江西师范大学数学与信息科学学院，南昌 330022
    2- 江西师范大学计算机信息工程学院，南昌 330022
    3- 江西科技学院，南昌 330098
    4- 江西财经大学信息管理学院，南昌 330013
  • 收稿日期:2014-04-21 接受日期:2015-05-28 出版日期:2015-10-15 发布日期:2015-12-15
  • 基金资助:
    国家自然科学基金 (71361015)；中国博士后基金 (2013M540534; 2014T70615)；教育部人文社科项目 (14YJC630085)；江西省自然科学基金 (20142BAB201013)；江西师范大学青年成长基金 (004796)；江西师范大学研究生创新基金 (2014010654).

Bayesian Estimation of TVaR Measure under Pareto-Gamma Models

ZHANG Yi1,2,  ZHOU Dong-qiong3,   WEN Li-min1,4   

  1. 1- College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022
    2- College of Computer and Information Engineering, Jiangxi Normal University, Nanchang 330022
    3- Jiangxi University of Technology, Nanchang 330098
    4- College of Information Management, Jiangxi University of Finance and Economics, Nanchang 330013
  • Received:2014-04-21 Accepted:2015-05-28 Online:2015-10-15 Published:2015-12-15
  • Supported by:
    The National Natural Science Foundation of China (71361015); the Postdoctoral Science Foundation of China (2013M540534; 2014T70615); the Humanities and Social Sciences Project of Ministry of Education (14YJC630085); the Natural Science Foundation of Jiangxi Province (20142BAB201013); the Youth Growth Fund of Jiangxi Normal University (004796); the Graduate Innovation Fund of Jiangxi Normal University (2014010654).

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摘要： 在金融风险管理中，对风险的度量及评估是决策者最为关心的问题．由于尾在险价值度量(TVaR)是一种改进的在险价值度量，又满足风险度量的一致性公理，因此TVaR在风险管理得到广泛的使用．本文对TVaR度量建立了贝叶斯统计模型，充分利用风险的样本信息与先验信息，给出了TVaR的贝叶斯估计，并证明了TVaR估计的强相合性．最后通过数值模拟的方法，计算了不同样本容量下贝叶斯估计的效率．结论表明，即使在样本容量较小的情况下，本文得到的估计仍然能满足实际使用的需要．

关键词: VaR度量, TVaR度量, 贝叶斯估计, 强相合性

Abstract:

In financial risk management, the measurement and assessment of risk are most concerned problems for decision makers. Since TVaR measure is not only an improved VaR measure, but also  meets the consistency axiom of risk measurement, TVaR has been widely used in risk management. In this paper, Bayesian statistical models are given by applying both the sample information and the prior information of risks. The Bayesian estimation is employed in this model, and the strong consistency of Bayesian estimation of TVaR is proved. Finally, the simulation methods are given to investigate the estimation efficiency for different sample sizes. The results indicate that the estimator is still able to meet the needs of actual applications even in the small sizes.

Key words: VaR measure, TVaR measure, Bayesian estimation, strong consistency

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