SIAM Journal on Financial Mathematics, Volume 11, Issue 1, Page 169-200, January 2020.
We incorporate a notion of risk aversion favoring prudent decisions from financial institutions into regulatory capital calculation principles. In the context of Basel III and IV as well as Solvency II, regulatory capital calculation is carried out through the tools of monetary risk measures. The notion of risk aversion that we focus on has four equivalent formulations: through consistency with second-order stochastic dominance, conditional expectations, or portfolio diversification, and through expected social impact. The class of monetary risk measures representing this notion of risk aversion is referred to as consistent risk measures. We characterize the class of consistent risk measures by establishing an Expected Shortfall (ES)-based representation, and as a by-product, we obtain new results on the representation of convex risk measures. We present several examples where consistent risk measures naturally appear. Using the obtained representation results, we study risk sharing and optimal investment problems and find several new analytical solutions.

中文翻译：

---

监管资本原则中的风险规避

SIAM金融数学杂志，第11卷，第1期，第169-200页，2020年1月。
我们将有利于金融机构审慎决策的风险规避概念纳入监管资本计算原则。在巴塞尔协议III和IV以及偿付能力标准II的背景下，监管资本的计算是通过货币风险衡量工具进行的。我们关注的风险规避概念有四个等效的表述：通过与二阶随机优势，条件性期望或投资组合多样化的一致性，以及通过预期的社会影响。代表此风险规避概念的货币风险衡量标准的类别称为一致性风险衡量标准。我们通过建立基于预期缺口（ES）的表示来表征一致风险度量的类别，作为副产品，我们在凸风险度量的表示中获得新的结果。我们提供了一些示例，这些示例中自然会出现一致的风险度量。使用获得的表示结果，我们研究了风险分担和最优投资问题，并找到了几种新的分析解决方案。