In this study, we propose new risk measures from a regulator’s perspective on the regulatory capital requirements. The proposed risk measures possess many desired properties, including monotonicity, translation-invariance, positive homogeneity, subadditivity, nonnegative loading, and stop-loss order preserving. The new risk measures not only generalize the existing, well-known risk measures in the literature, including the Dutch, tail value-at-risk (TVaR), and expectile measures, but also provide new approaches to generate feasible and practical coherent risk measures. As examples of the new risk measures, TVaR-type generalized expectiles are investigated in detail. In particular, we present the dual and Kusuoka representations of the TVaR-type generalized expectiles and discuss their robustness with respect to the Wasserstein distance.

中文翻译：

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从监管机构对保险公司监管资本要求的角度得出的风险措施

在本研究中，我们从监管机构的角度提出了监管资本要求的新风险措施。所提出的风险度量具有许多期望的属性，包括单调性、平移不变性、正同质性、次可加性、非负加载和止损顺序保持。新的风险度量不仅概括了文献中现有的、众所周知的风险度量，包括荷兰、尾部风险价值 (TVaR) 和预期度量，而且还提供了生成可行和实用的连贯风险度量的新方法. 作为新风险度量的示例，详细研究了 TVaR 型广义期望值。特别是，我们提出了 TVaR 型广义期望的对偶和 Kusuoka 表示，并讨论了它们对 Wasserstein 距离的鲁棒性。