论文标题
用于风险评估和强大优化的模型聚合
Model Aggregation for Risk Evaluation and Robust Optimization
论文作者
论文摘要
我们引入了一种基于随机优势的审慎风险评估的新方法，该方法将称为模型聚合（MA）方法。与经典的最坏风险（WR）方法相反，MA方法不仅产生了风险评估的强大价值，而且还产生了与任何特定风险措施无关的强大分配模型。 MA风险评估可以通过随机优势的晶格理论中的明确公式来计算，并且在某些标准假设下，MA强大的优化允许凸出程序重新构造。 Wasserstein和均值变化不确定性集的MA方法集合获得了获得的强大模型的明确公式。通过MA和WR进近之间的等效性能，获得了新的公理特性，即具有价值（VAR）和预期的不足（ES，也称为CVAR）的新公理表征。通过投资组合优化的各种风险措施和示例来说明新方法。
We introduce a new approach for prudent risk evaluation based on stochastic dominance, which will be 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 the WR approaches, new axiomatic characterizations are obtained for the Value-at-Risk (VaR) and the Expected Shortfall (ES, also known as CVaR). The new approach is illustrated with various risk measures and examples from portfolio optimization.
