英文标题：
《Liquidity, risk measures, and concentration of measure》
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作者：
Daniel Lacker
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最新提交年份：
2015
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英文摘要：
Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(\\rho(\\lambda X))_{\\lambda \\ge 0}$, where $\\rho$ is a convex risk measure and $X$ a random variable, and we call such a curve a \\emph{liquidity risk profile}. The shape of a liquidity risk profile is intimately linked with the tail behavior of the underlying $X$ for some notable classes of risk measures, namely shortfall risk measures. We exploit this link to systematically bound liquidity risk profiles from above by other real functions $\\gamma$, deriving tractable necessary and sufficient conditions for \\emph{concentration inequalities} of the form $\\rho(\\lambda X) \\le \\gamma(\\lambda)$, for all $\\lambda \\ge 0$. These concentration inequalities admit useful dual representations related to transport inequalities, and this leads to efficient uniform bounds for liquidity risk profiles for large classes of $X$. On the other hand, some modest new mathematical results emerge from this analysis, including a new characterization of some classical transport-entropy inequalities. Lastly, the analysis is deepened by means of a surprising connection between time consistency properties of law invariant risk measures and the tensorization of concentration inequalities.
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中文摘要：
通过扩展度量集中度技术，我们开发了一个定量框架，用于使用凸风险度量对流动性风险进行建模。研究的基本对象是$（\\rho（\\lambda X））{\\lambda\\ge 0}$形式的曲线，其中$\\rho$是一个凸风险度量，而$X$是一个随机变量，我们称这种曲线为流动性风险曲线。对于某些值得注意的风险度量类别，即短缺风险度量，流动性风险状况的形状与潜在美元X美元的尾部行为密切相关。我们利用这个链接，通过其他实函数$\\gamma$从上面系统地约束流动性风险曲线，推导出所有$\\lambda\\ge 0$的$\\rho（\\lambda X）\\le\\gamma（\\lambda）$形式的$\\emph{concentration不等式}可处理的充分必要条件。这些集中度不平等承认了与运输不平等有关的有用的对偶表示，这导致了大类$X$的流动性风险曲线的有效统一界限。另一方面，从这个分析中产生了一些新的数学结果，包括一些经典输运熵不等式的新特征。最后，通过法律不变风险测度的时间一致性性质与集中不等式的张量化之间令人惊讶的联系，深化了分析。
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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：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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