Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2015, Vol. 32 ›› Issue (5): 667-676.doi: 10.3969/j.issn.1005-3085.2015.05.005

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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).

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

CLC Number: