论文标题
具有功能优化的均值变化投资组合管理
Mean-Variance Portfolio Management with Functional Optimization
论文作者
论文摘要
本文通过将未知的权重矢量视为过去值的函数，而不是将它们视为大多数研究中的固定未知系数，从而引入了一种新的功能优化方法来进行投资组合优化问题。我们首先表明最佳解决方案通常不是恒定函数。我们给出了向量函数作为解决方案的最佳条件，因此给出了插件解决方案的条件（根据过去值替换未知的均值和差异）是最佳的。在表明插件解决方案通常是亚最佳的之后，我们提出了梯度呈梯度算法，以使用提供的融合定理来解决均值变化投资组合管理的功能优化。模拟和实证研究表明，我们的方法的性能要比插件方法要好得多。
This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of studies. We first show that the optimal solution, in general, is not a constant function. We give the optimal conditions for a vector function to be the solution, and hence give the conditions for a plug-in solution (replacing the unknown mean and variance by certain estimates based on past values) to be optimal. After showing that the plug-in solutions are sub-optimal in general, we propose gradient-ascent algorithms to solve the functional optimization for mean-variance portfolio management with theorems for convergence provided. Simulations and empirical studies show that our approach can perform significantly better than the plug-in approach.
