Model Aggregation for Risk Evaluation and Robust Optimization
提出基于随机占优的模型聚合方法，相比经典最坏情况风险方法，能同时给出稳健风险值和稳健分布模型，且可通过显式公式计算，适用于投资组合优化等场景。
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. This paper was accepted by Chung Piaw Teo, optimization. Funding: This research was supported by the National Natural Science Foundation of China [Grants 12371476, 71921001, 71671176, 71871208], the Natural Sciences and Engineering Research Council of Canada [Grants CRC-2022-00141, RGPIN-2024-03728, RGPAS-2018-522590, RGPIN-2018-03823], and the Society of Actuaries Center of Actuarial Excellence Research Grant. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03523 .