Optimizing distortion riskmetrics with distributional uncertainty

• 成果类型: Article
• 署名作者: Pesenti, Silvana M.; Wang, Qiuqi; Wang, Ruodu
• 署名单位: University of Toronto; University System of Georgia; Georgia State University; University of Waterloo
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-024-02128-6
• 发表日期: 2025
• 页码: 51-106
• 关键词: value-at-risk; model uncertainty; robust; REPRESENTATION; optimization; INFORMATION; bounds; inequalities; aggregation; CHOICE

摘要

Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not necessarily monotone or convex. One of our central findings is a unifying result that allows to convert an optimization of a non-convex distortion riskmetric with distributional uncertainty to a convex one induced from the concave envelope of the distortion function, leading to practical tractability. A sufficient condition to the unifying equivalence result is the novel notion of closedness under concentration, a variation of which is also shown to be necessary for the equivalence. Our results include many special cases that are well studied in the optimization literature, including but not limited to optimizing probabilities, Value-at-Risk, Expected Shortfall, Yaari's dual utility, and differences between distortion risk measures, under various forms of distributional uncertainty. We illustrate our theoretical results via applications to portfolio optimization, optimization under moment constraints, and preference robust optimization.