风险度量ES半参数模型估计及其应用  

Semiparametric Estimation of Expected Shortfall and Its Application

作　　者：管欣 周勇[2] GUAN Xin;ZHOU Yong(School of Statistics and Management,Shanghai University of Finance and Economics,Shanghai 200433,China;Academy of Statistics and Interdisciplinary Sciences,East China Normal University,Shanghai 200062,China)

机构地区：[1]上海财经大学统计与管理学院,上海200433 [2]华东师范大学经管学部交叉科学研究院及统计学院,上海200062

出　　处：《应用数学学报》2019年第6期744-760,共17页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学重大研究计划重点项目(91546202);国家自然科学基金委重点项目(71931004);上海财经大学研究生创新计划(CXJJ-2017-430)资助项目

摘　　要：预期不足或称期损(Expected Shortfall,ES)是近几年发展起来的重要风险度量工具,对其进行建模和估计是统计学和金融计量经济学研究的前沿问题之一.本文基于平均剩余寿命模型提出一种ES估计的半参数模型,并使用广义估计方程(GEE)的方法估计参数.同时建立了严平稳a混合相依序列下参数估计的大样本理论.本文模型的意义在于可以研究资产组合的风险来源以及各风险因素对ES大小的影响程度.最后,将本文的模型应用到金融股票市场的风险评估中,结果表明此模型可以对某些金融市场现象作出合理的解释,是一个灵活且合理的金融计量统计模型.Expected shortfall(ES) is an important risk measurement tool and has gainedincreasingly popularity in financial risk management. ES estimation is a frontier topic instatistical and financial econometrie research. Previous studies on ES estimation mainlyconcentrated in parametrie model set-ups or nonparametric approach, and ignored exoge・nous factors. In this paper, we develop a semiparametric approach for modeling ES basedon the Mean Residual Life (MRL) model. One important contribution of this model is thatwe can find out the source of risk factors and their importance for a portfolio. We adapt thegeneralized estimating equation (GEE) met hod to estimate the coefficient functions and extendtheir asymptotic results to allow for strictly stationary alpha mixing conditions. As anillustration, we apply the proposed model to the risk assessment of both simulated and realdata. The results show that this model can make a reasonable explanation on the generalfinancial market phenomenon and is worth to study further, such as extending this modelto include additive factors and so forth.

关 键 词：预期不足 a混合 平均剩余寿命模型 

分 类 号：O212.7[理学—概率论与数理统计]