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.

中文翻译：

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具有功能优化的均值-方差投资组合管理

本文介绍了一种新的函数优化方法来解决投资组合优化问题，将未知权重向量视为过去值的函数，而不是在大多数研究中将它们视为固定的未知系数。我们首先表明，一般来说，最优解不是一个常数函数。我们给出了向量函数成为解的最优条件，因此给出了插件解（用基于过去值的某些估计值替换未知均值和方差）最优的条件。在证明插件解决方案通常是次优的之后，我们提出梯度上升算法来解决均值方差投资组合管理的功能优化，并提供收敛定理。