英文标题：
《Unbiased estimation of risk》
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作者：
Marcin Pitera and Thorsten Schmidt
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最新提交年份：
2017
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英文摘要：
The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures of risk measures in terms of bias. We show that once the parameters of a model need to be estimated, one has to take additional care when estimating risks. The typical plug-in approach, for example, introduces a bias which leads to a systematic underestimation of risk. In this regard, we introduce a novel notion of unbiasedness to the estimation of risk which is motivated by economic principles. In general, the proposed concept does not coincide with the well-known statistical notion of unbiasedness. We show that an appropriate bias correction is available for many well-known estimators. In particular, we consider value-at-risk and expected shortfall (tail value-at-risk). In the special case of normal distributions, closed-formed solutions for unbiased estimators can be obtained. We present a number of motivating examples which show the outperformance of unbiased estimators in many circumstances. The unbiasedness has a direct impact on backtesting and therefore adds a further viewpoint to established statistical properties.
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中文摘要：
风险度量的估计最近得到了很多关注，部分原因是与可引出性相关的预期不足的回溯测试问题。在这项工作中，我们从偏差的角度对风险度量的最佳估计程序进行了新的、基本的阐述。我们表明，一旦需要估计模型的参数，在估计风险时就必须格外小心。例如，典型的插件方法引入了一种偏见，导致系统性地低估风险。在这方面，我们引入了一种新的无偏性概念来估计风险，其动机是经济原则。一般来说，提出的概念与众所周知的无偏统计概念并不一致。我们证明，对于许多著名的估计量，适当的偏差校正是可用的。特别是，我们考虑了风险价值和预期短缺（风险尾值）。在正态分布的特殊情况下，可以得到无偏估计的闭式解。我们给出了一些激励性的例子，表明在许多情况下无偏估计的性能优于无偏估计。无偏性对回溯测试有直接影响，因此为已建立的统计特性添加了进一步的观点。
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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：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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