英文标题：
《Time-consistency of risk measures with GARCH volatilities and their
estimation》
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作者：
Claudia Kl\\\"uppelberg, Jianing Zhang
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最新提交年份：
2016
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英文摘要：
In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study in detail our construction for the risk measures Value-at-Risk (VaR) and Average Value-at-Risk (AVaR). While in the VaR case we can derive an analytical formula for its time-consistent counterpart, in the AVaR case we derive lower and upper bounds to its time-consistent version. Furthermore, we incorporate techniques from Extreme Value Theory (EVT) to allow for a more tail-geared statistical analysis of the corresponding risk measures. We conclude with an application of our results to a data set of stock prices.
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中文摘要：
本文研究了GARCH（1,1）模型给出的收益率的时间一致性风险度量。我们提出了一种基于静态度量的风险度量结构，克服了时间一致性的不足。然后，我们详细研究了风险度量值（VaR）和平均风险值（AVaR）的构造。而在VaR情况下，我们可以推导出其时间一致性对应物的分析公式，在AVaR情况下，我们推导出其时间一致性版本的上下限。此外，我们还结合了极值理论（EVT）的技术，以便对相应的风险度量进行更具尾部的统计分析。最后，我们将我们的结果应用于股票价格数据集。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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