A One-Layer Neural Network for Robust Mean-Variance Portfolio Selection Problem

Driven by globalization and technological innovation, the financial markets have experienced unprecedented volatility and uncertainty. Portfolio selection is a fundamental strategy in finance. During recent decades, the frequent occurrence of extreme market events and uncertainties has exposed significant limitations in the traditional mean-variance model, emphasizing the critical need for more robust approaches. In response to these challenges, this paper introduces a neurodynamic approach to robust portfolio selection. This approach is capable of efficiently handling high-dimensional data through massively parallel processing, providing a resilient solution to the complexities of modern financial markets. First, the corresponding robust counterpart model is derived by eliminating uncertainty from the robust portfolio selection model under the box uncertainty set. Consequently, the robust portfolio selection problem is transformed into a solvable quadratic programming problem. Next, a one-layer neural network model is constructed based on the Karush-Kuhn-Tucker (KKT) conditions. Subsequently, the stability and convergence of the proposed neural network are analyzed. Finally, simulation experiments are conducted using two global stock market datasets. The proposed neural network model demonstrates convergence even with large-scale data in the second dataset, highlighting the effectiveness of the neurodynamic approach in addressing robust portfolio selection problems.