Distortion risk measures: Prudence, coherence, and the expected shortfall
系统研究了扭曲风险度量，基于定性稳健性、审慎性、无集中奖励和尾部相关性等新概念，刻画了审慎扭曲风险度量、给出了一致扭曲风险度量的新表示以及预期亏损的公理化，为风险管理提供了新视角。
Abstract Distortion risk measures (DRM) are risk measures that are law invariant and comonotonic additive. The present paper is an extensive inquiry into this class of risk measures in light of new ideas such as qualitative robustness, prudence and no reward for concentration, and tail relevance. Results include several characterizations of prudent DRMs, a novel representation of coherent DRMs as well as an axiomatization of the Expected Shortfall alternative to the one recently provided by Wang and Zitikis. By linking the two axiomatizations, the paper provides a new perspective on the idea of no reward for concentration. The paper also contains results of independent interest such as the lower semicontinuity with respect to convergence in distribution of the Haezendonck–Goovaerts risk measures, the extension of non‐necessarily convex risk measures as well as the structure of the core of a general submodular distortion.