Model Aggregation for Risk Evaluation and Robust Optimization

• 成果类型: Article
• 署名作者: Mao, Tiantian; Wang, Ruodu; Wu, Qinyu
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Waterloo
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2023.03523
• 发表日期: 2026
• 关键词: value at risk; expected shortfall; stochastic dominance; model aggregation; worst case risk measures; model uncertainty; robust optimization

摘要

We introduce a new approach for prudent risk evaluation based on stochastic dominance, and it is called the model aggregation (MA) approach. In contrast to the classic worst case risk (WR) approach, the MA approach produces not only a robust value of risk evaluation but also a robust distributional model, independent of any specific risk measure. The MA risk evaluation can be computed through explicit formulas in the lattice theory of stochastic dominance, and under some standard assumptions, the MA robust optimization admits a convex program reformulation. The MA approach for Wasserstein and mean-variance uncertainty sets admits explicit formulas for the obtained robust models. Via an equivalence property between the MA and WR approaches, new axiomatic characterizations are obtained for the value at risk and the expected shortfall (also known as conditional value at risk). The new approach is illustrated with various risk measures and examples from portfolio optimization.