Bayes risk, elicitability, and the Expected Shortfall
Bayes risk, elicitability, and the Expected Shortfall
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DOI：
10.1111/mafi.12313
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发表时间：
2020-10
影响因子：
1.6
通讯作者：
P. Embrechts;Tiantian Mao;Qiuqi Wang;Ruodu Wang
中科院分区：
文献类型：
--
作者：
P. Embrechts;Tiantian Mao;Qiuqi Wang;Ruodu Wang
基于风险度量的可导出性和风险优化的实际考虑，我们引入了贝叶斯对和贝叶斯风险度量的概念。贝叶斯风险度量是导出风险度量的对应物，在最近的文献中得到了广泛的研究。预期缺口（ES）是金融、保险、风险管理和工程等行业实践和学术研究中最重要的一致性风险度量。我们的一个中心结果是，在连续性条件下，ES是唯一的一类相干贝叶斯风险措施。我们进一步表明，熵风险措施是唯一的风险措施，这是既引出和贝叶斯。其他几个理论性质和开放的问题贝叶斯风险措施进行了讨论。
Motivated by recent advances on elicitability of risk measures and practical considerations of risk optimization, we introduce the notions of Bayes pairs and Bayes risk measures. Bayes risk measures are the counterpart of elicitable risk measures, extensively studied in the recent literature. The Expected Shortfall (ES) is the most important coherent risk measure in both industry practice and academic research in finance, insurance, risk management, and engineering. One of our central results is that under a continuity condition, ES is the only class of coherent Bayes risk measures. We further show that entropic risk measures are the only risk measures which are both elicitable and Bayes. Several other theoretical properties and open questions on Bayes risk measures are discussed.