发表机构
Cornell University; Columbia University（康奈尔大学; 哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对谱风险度量下的投资组合估计，提出了一种数据自适应的高效估计方法，通过优化谱度量选择提升估计效率，并验证了其有效性。
AI 中文摘要
谱风险度量，包括条件风险价值（CVaR），为投资组合估计生成了一族凸准则。我们研究了当不同准则共享同一总体极小化器时，应如何选择准则，以及高效准则本身是否可以从数据中学习。我们在估计的线性约束下，为经验谱风险最小化发展了一种一般渐近理论。在正态尺度混合椭圆回报下，所有谱风险度量识别出相同的总体有效投资组合，但它们的经验极小化器具有不同的抽样分布。它们的渐近协方差分解为一个公共分量和一个由谱度量的泛函缩放的正半定分量，将效率问题简化为对概率测度的优化。我们刻画了效率最优的谱度量，并表明单层CVaR通常是低效的。然后，我们构建了一个完全数据自适应的估计器，它从用于投资组合估计的同一观测中学习径向分布和最优谱度量，却与不可行的预言机具有相同的一阶分布。模拟和实证应用说明了该方法。
英文摘要
Spectral risk measures, including conditional value-at-risk (CVaR), generate a family of convex criteria for portfolio estimation. We study how the criterion should be chosen when different criteria share the same population minimizer, and whether the efficient criterion can itself be learned from data. We develop a general asymptotic theory for empirical spectral-risk minimization under estimated linear constraints. Under normal scale-mixture elliptical returns, all spectral risk measures identify the same population efficient portfolio, but their empirical minimizers have different sampling distributions. Their asymptotic covariance decomposes into a common component and a positive-semidefinite component scaled by a functional of the spectral measure, reducing efficiency to an optimization over probability measures. We characterize the efficiency-optimal spectral measure and show that single-level CVaR is generally inefficient. We then construct a fully data-adaptive estimator that learns the radial distribution and optimal spectral measure from the same observations used for portfolio estimation, yet has the same first-order distribution as the infeasible oracle. Simulations and an empirical application illustrate the method.
Comments107 pages, 4 figures, 3 tables
