论文标题
调整后的预期不足
Adjusted Expected Shortfall
论文作者
论文摘要
我们介绍和研究一类凸风险度量的主要特性，通过同时控制与尾巴分布的不同部分相关的预期损失，从而完善了预期的不足。相应的调整后的预期短缺将风险量化为必须筹集并注入财务位置$ x $的最低资本量，以确保预期的短缺$ eS_p（x）$不超过预先指定的阈值$ g（p）$，对于每个概率级别$ p \ in [0,1] $。通过选择基准风险概况$ g $，一个人可以根据利益的特定应用来量身定制风险评估。我们特别注意由基准随机损失的预期缺口定义的风险概况的研究，在这种情况下，我们的风险措施与二阶随机占优势密切相关。
We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding adjusted Expected Shortfalls quantify risk as the minimum amount of capital that has to be raised and injected into a financial position $X$ to ensure that Expected Shortfall $ES_p(X)$ does not exceed a pre-specified threshold $g(p)$ for every probability level $p\in[0,1]$. Through the choice of the benchmark risk profile $g$ one can tailor the risk assessment to the specific application of interest. We devote special attention to the study of risk profiles defined by the Expected Shortfall of a benchmark random loss, in which case our risk measures are intimately linked to second-order stochastic dominance.
