论文标题
反向ES（CVAR）优化公式
A reverse ES (CVaR) optimization formula
论文作者
论文摘要
著名的预期缺口（ES）优化公式意味着固定概率水平的ES是线性真实函数的最小值以及缩放的平均多余函数。我们建立一个反向ES优化公式，该公式说，在任何固定阈值下的平均多余函数是ES曲线的最大值减去线性函数。尽管是一个简单的结果，但该公式仍揭示了平均多余功能与ES曲线及其优化器之间的优雅对称性。反向ES优化公式与Fenchel-Legendre变换密切相关，我们的公式从ES推广到优化确定性等效物，这是一种流行的凸风险度量。我们在两个流行的模型不确定性设置下分析了平均多余功能的最坏情况值，以说明反向ES优化公式的有用性，并且使用保险数据集的应用程序进一步证明了这一点。
The celebrated Expected Shortfall (ES) optimization formula implies that ES at a fixed probability level is the minimum of a linear real function plus a scaled mean excess function. We establish a reverse ES optimization formula, which says that a mean excess function at any fixed threshold is the maximum of an ES curve minus a linear function. Despite being a simple result, this formula reveals elegant symmetries between the mean excess function and the ES curve, as well as their optimizers. The reverse ES optimization formula is closely related to the Fenchel-Legendre transforms, and our formulas are generalized from ES to optimized certainty equivalents, a popular class of convex risk measures. We analyze worst-case values of the mean excess function under two popular settings of model uncertainty to illustrate the usefulness of the reverse ES optimization formula, and this is further demonstrated with an application using insurance datasets.
