风险集中与均值-预期损失准则
Risk Concentration and the Mean-Expected Shortfall Criterion
摘要：
预期损失（ExpectedShortfall，ES，又称CVaR）是金融、保险、风险管理和工程等领域最重要的一致性风险度量。最近，Wang和Zitikis（2021）提出了投资组合风险评估的四个经济公理，为ES族提供了第一个经济公理基础。特别是，集中度无报酬公理（NRC）可以说是相当强的，它对具有某种依赖结构的投资组合施加了一种附加形式的风险度量。我们从NRC公理出发，引入了集中厌恶的概念，它不强加任何特定形式的风险度量。证明了具有集中规避的风险测度是ES和期望的函数。与其他三个标准公理单调性，平移不变性和下连续性，浓度厌恶唯一的特点家庭ES。此外，我们建立了一个公理化的基础上的问题的均值ES投资组合选择和新的显式公式凸和一致的风险措施。最后，我们提供了一个经济的理由集中厌恶通过几个公理的监管机构对依赖结构的态度。
英文摘要：
Expected Shortfall (ES, also known as CVaR) is the most important coherent risk measure in finance, insurance, risk management, and engineering. Recently, Wang and Zitikis (2021) put forward four economic axioms for portfolio risk assessment and provide the first economic axiomatic foundation for the family of ES. In particular, the axiom of no reward for concentration (NRC) is arguably quite strong, which imposes an additive form of the risk measure on portfolios with a certain dependence structure. We move away from the axiom of NRC by introducing the notion of concentration aversion, which does not impose any specific form of the risk measure. It turns out that risk measures with concentration aversion are functions of ES and the expectation. Together with the other three standard axioms of monotonicity, translation invariance and lower semicontinuity, concentration aversion uniquely characterizes the family of ES. In addition, we establish an axiomatic foundation for the problem of mean-ES portfolio selection and new explicit formulas for convex and consistent risk measures. Finally, we provide an economic justification for concentration aversion via a few axioms on the attitude of a regulator towards dependence structures.
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