Cash-Subadditive Risk Measures Without Quasi-Convexity

• 成果类型: Article; Early Access
• 署名作者: Han, Xia; Wang, Qiuqi; Wang, Ruodu; Xia, Jianming
• 署名单位: Nankai University; Nankai University; University System of Georgia; Georgia State University; University of Waterloo; Chinese Academy of Sciences
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0312
• 发表日期: 2025
• 关键词: representation; Allocations; Robustness; management; ambiguity; aversion

摘要

In the literature on risk measures, cash subadditivity was proposed to replace cash additivity, motivated by the presence of stochastic or ambiguous interest rates and defaultable contingent claims. Cash subadditivity has been traditionally studied together with quasi-convexity, in a way similar to cash additivity with convexity. In this paper, we study cash-subadditive risk measures without quasi-convexity. One of our major results is that a general cash-subadditive risk measure can be represented as the lower envelope of a family of quasi-convex and cash-subadditive risk measures. Representation results of cashsubadditive risk measures with some additional properties are also examined. The notion of quasi-star-shapedness, which is a natural analogue of star-shapedness, is introduced, and we obtain a corresponding representation result via the lower envelope of normalized, quasi-convex, and cash-subadditive risk measures.