Neurodynamic Approaches to Cardinality-Constrained Portfolio Optimization

The field of portfolio optimization holds significant interest for both academic researchers and financial practitioners. Markowitz's seminal mean–variance analysis laid the groundwork for optimizing portfolios by balancing returns and risks, marking a pivotal advancement in investment strategy formulation. However, despite its foundational role, mean–variance theory is not without its limitations, notably its reliance on assumptions that do not always hold in real-world scenarios and its use of variance as a risk measure, which may not fully capture the complexities of risk behaviors. The pursuit of alternative risk measures introduces mathematical and computational challenges due to nonconvexity and discontinuities. Concurrently, the field of neural networks has seen vigorous activity, particularly with the advancements in deep learning, offering novel approaches to a variety of optimization problems. Within this stream, neurodynamic optimization emerges as a method that leverages the parallel and distributed computing capabilities of neural networks, proving to be effective for tackling global optimization, multi-period, and multi-objective problems, and is now expanding into bi-level and combinatorial optimization domains. Given these developments, applying neurodynamic optimization to portfolio optimization is a promising avenue, especially considering the unique challenges posed by the financial domain in terms of complexity and scale. This chapter delves into the application of neurodynamic optimization to portfolio optimization, specifically focusing on cardinality-constrained problems. Through experimental analysis across several global stock market datasets, neurodynamic systems have demonstrated their efficacy in achieving superior performance based on key metrics. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.