Bayes risk, elicitability, and the Expected Shortfall
受风险度量可引致性和风险优化实践的启发，引入贝叶斯对和贝叶斯风险度量的概念，证明在连续性条件下预期亏损是唯一的一类一致贝叶斯风险度量，并指出熵风险度量是唯一同时具有可引致性和贝叶斯性的风险度量。
Abstract 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.