论文标题
通过分配不确定性优化失真风险对象
Optimizing distortion riskmetrics with distributional uncertainty
论文作者
论文摘要
用分布不确定性优化失真风险对象在金融和运营研究中广泛应用。失真风险对数包括许多常用的风险措施和偏差措施，这些措施不一定是单调或凸。我们的中心发现之一是一个统一的结果，它使我们能够转换对凸的非凸变形风险的优化，分布不确定性，从而导致了极大的障碍。统一等效结果的充分条件是浓度下的闭合度的新概念，其变异也被证明是等效性所必需的。我们的结果包括许多在优化文献中进行了充分研究的特殊情况，包括但不限于优化概率，价值风险，预期短缺，Yaari的双重效用以及在各种形式的分布不确定性下，扭曲风险度量之间的差异。我们通过应用投资组合优化，在矩限制下的优化以及优先优化的优化来说明我们的理论结果。
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not necessarily monotone or convex. One of our central findings is a unifying result that allows us to convert an optimization of a non-convex distortion riskmetric with distributional uncertainty to a convex one, leading to great tractability. A sufficient condition to the unifying equivalence result is the novel notion of closedness under concentration, a variation of which is also shown to be necessary for the equivalence. Our results include many special cases that are well studied in the optimization literature, including but not limited to optimizing probabilities, Value-at-Risk, Expected Shortfall, Yaari's dual utility, and differences between distortion risk measures, under various forms of distributional uncertainty. We illustrate our theoretical results via applications to portfolio optimization, optimization under moment constraints, and preference robust optimization.
