Contextual Areas Star-Shaped Risk Measures

• 成果类型: Article; Early Access
• 署名作者: Castagnoli, Erio; Cattelan, Giacomo; Maccheroni, Fabio; Tebaldi, Claudio; Wang, Ruodu
• 署名单位: Bocconi University; New York University; Bocconi University; University of Waterloo
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2303
• 发表日期: 2022
• 关键词: convexity; capital charge; liquidity risk; Competitive pricing; monotonicity along rays

摘要

In this paper, monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties are studied. The measures in this class, which arise when the subadditivity property of coherent risk measures is dispensed with and positive homogeneity is weakened, include all practically used risk measures, in particular, both convex risk measures and value-at-risk. From a financial viewpoint, our relaxation of convexity is necessary to quantify the capital requirements for risk exposure in the presence of liquidity risk, competitive delegation, or robust aggregation mechanisms. From a decision theoretical perspective, star-shaped risk measures emerge from variational preferences when risk mitigation strategies can be adopted by a rational decision maker.