Introduction to the Theory of Probabilistic Functions and Percentiles (Value-at-Risk)
Introduction to the Theory of Probabilistic Functions and Percentiles (Value-at-Risk)
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DOI：
10.1007/978-1-4757-3150-7_1
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发表时间：
2000
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影响因子：
--
通讯作者：
S. Uryasev
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文献类型：
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作者：
S. Uryasev
概率和分位数（百分位数）函数通常用于分析具有不确定性或参数可变性的模型。在金融应用中，损失的百分位数被称为风险价值（VaR）。VaR是一种广泛使用的业绩衡量指标，它回答了这样一个问题：在特定的置信水平下，最大损失是多少？百分位数还用于定义其他相关的绩效度量，例如条件风险价值（CVaR）。CVaR（也称为平均超额损失、平均缺口或尾部VaR）是指x%最坏情况下（例如5%）的平均损失。与VaR相比，CVaR风险度量具有更吸引人的特性。本文给出了CVaR风险度量的基本定义，并回顾了几个主题：概率函数的敏感性；百分位敏感性（VaR）；CVaR的优化方法。本文的重点是最近才发展起来的问题。
Probabilistic and quantile (percentile) functions are commonly used for the analysis of models with uncertainties or variabilities in parameters. In financial applications, the percentile of the losses is called Value-at-Risk (VaR). VaR, a widely used performance measure, answers the question: what is the maximum loss with a specified confidence level? Percentiles are also used for defining other relevant performance measures, such as Conditional Value-at-Risk (CVaR). CVaR (also called Mean Excess Loss, Mean Shortfall, or Tail VaR) is the average loss for the worst x% scenarios (e.g., 5%). CVaR risk measure has more attractive properties compared to VaR. This introductory paper gives basic definitions and reviews several topics:sensitivities of probabilistic functions;sensitivities of percentiles (VaR);optimization approaches for CVaR.The emphasis of this paper is on issues which have been relatively recently developed.