School of Science and Technology, Hong Kong Metropolitan University, Kowloon, Hong Kong.
Department of Computer Science and School of Data Science, City University of Hong Kong, Kowloon, Hong Kong.
Neural Netw. 2022 Jan;145:68-79. doi: 10.1016/j.neunet.2021.10.007. Epub 2021 Oct 25.
Portfolio optimization is one of the most important investment strategies in financial markets. It is practically desirable for investors, especially high-frequency traders, to consider cardinality constraints in portfolio selection, to avoid odd lots and excessive costs such as transaction fees. In this paper, a collaborative neurodynamic optimization approach is presented for cardinality-constrained portfolio selection. The expected return and investment risk in the Markowitz framework are scalarized as a weighted Chebyshev function and the cardinality constraints are equivalently represented using introduced binary variables as an upper bound. Then cardinality-constrained portfolio selection is formulated as a mixed-integer optimization problem and solved by means of collaborative neurodynamic optimization with multiple recurrent neural networks repeatedly repositioned using a particle swarm optimization rule. The distribution of resulting Pareto-optimal solutions is also iteratively perfected by optimizing the weights in the scalarized objective functions based on particle swarm optimization. Experimental results with stock data from four major world markets are discussed to substantiate the superior performance of the collaborative neurodynamic approach to several exact and metaheuristic methods.
投资组合优化是金融市场中最重要的投资策略之一。对于投资者，特别是高频交易者来说，在投资组合选择中考虑基数约束以避免零股和过高的成本（如交易费用）是非常理想的。本文提出了一种用于基数约束投资组合选择的协同神经动力学优化方法。马克维茨框架中的预期收益和投资风险被标量化为加权切比雪夫函数，基数约束通过引入二进制变量并将其作为上限来等效表示。然后，基数约束投资组合选择被表述为一个混合整数优化问题，并通过使用粒子群优化规则多次重新定位的多个递归神经网络的协同神经动力学优化来解决。基于粒子群优化优化标量化目标函数中的权重，迭代完善所得帕累托最优解的分布。通过对来自四个主要世界市场的股票数据进行实验，讨论了协同神经动力学方法相对于几种精确和元启发式方法的优越性能。
