arXiv 2201.063702022-01q-fin.RM

基于模型聚合的风险评估与鲁棒优化

Model Aggregation for Risk Evaluation and Robust Optimization

Tiantian Mao, Ruodu Wang, Qinyu Wu

AI总结：

本文提出基于随机占优的模型聚合（MA）方法，用于审慎风险评估与鲁棒优化，能同时给出鲁棒风险值和独立于风险度量的鲁棒分布模型，并为VaR和ES提供新的公理化刻画。

摘要：

我们引入一种基于随机占优的审慎风险评估新方法，称为模型聚合（MA）方法。与经典的worst-case risk（WR）方法相比，MA方法不仅产生鲁棒的风险评估值，还产生一个独立于任何特定风险度量的鲁棒分布模型。MA风险评估可以通过随机占优格理论中的显式公式计算，并且在某些标准假设下，MA鲁棒优化可转化为凸规划重构。针对Wasserstein和均值-方差不确定性集合的MA方法，所获得的鲁棒模型具有显式公式。通过MA与WR方法之间的等价性质，我们为Value-at-Risk（VaR）和Expected Shortfall（ES，也称为CVaR）获得了新的公理化刻画。我们用各种风险度量和投资组合优化示例来说明这一新方法。

英文摘要：

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.

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