• 论文 •

### 高维投资组合风险的估计

1. 贵州财经大学数学与统计学院, 贵阳 550025
• 出版日期:2018-08-25 发布日期:2018-10-12

LIU Liping. Estimation of High Dimensional Portfolio Risk[J]. Journal of Systems Science and Mathematical Sciences, 2018, 38(8): 919-930.

### Estimation of High Dimensional Portfolio Risk

LIU Liping

1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025
• Online:2018-08-25 Published:2018-10-12

In the era of big data, it is a big challenge for financial institutions to estimate the risk of high dimensional portfolios. This thesis~focused~on~the~following~two~aspects: Firstly, the non-linear shrinkage method and the QuEST function are applied to the BEKK model, and a new covariance matrix estimation and prediction model --- BEKK-NS is proposed to estimate and predict the covariance matrix that plays an important role in the portfolio. The model not only can be used to estimate the covariance matrix of the normal distribution and the heavy tailed distribution, but also can solve the curse of dimensionality and improve the efficiency of the covariance matrix; Secondly, the limit errors $\hat {U}(\alpha )$ which is based on block bootstrap method is constructed to evaluate the risk of the large portfolio. It is found through simulation and empirical researches that the BEKK-NS model is better than the BEKK model, investors can reduce risk and get higher returns when the BEKK-NS model is applied in portfolio; Moreover, the limit error constructed in this paper is very close to the real error, and the confidence interval of the portfolio risk constructed by $\hat {U}(\alpha )$ is more accurate.

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