Abstract This paper focuses on the computation issue of portfolio optimization with scenario-based Value-at-Risk. The main idea is to replace the portfolio selection models with linear programming problems. According to the convex optimization theory and some concepts of ordinary differential equations, a neural network model for solving linear programming problems is presented. The equilibrium point of the proposed model is proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the portfolio selection problem with uncertain returns. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.

中文翻译：

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基于人工神经网络方案的具有风险价值和不确定回报的投资组合管理

摘要 本文重点研究基于情景的风险价值的投资组合优化的计算问题。主要思想是用线性规划问题代替投资组合选择模型。根据凸优化理论和常微分方程的一些概念，提出了求解线性规划问题的神经网络模型。证明了所提出模型的平衡点等价于原问题的最优解。还表明，所提出的神经网络模型在 Lyapunov 意义上是稳定的，并且它全局收敛到具有不确定回报的投资组合选择问题的精确最优解。提供了几个说明性例子来说明本文所提出方法的可行性和效率。