Cardinality-constrained Portfolio Selection via Two-timescale Duplex Neurodynamic Optimization

This paper addresses portfolio selection based on neurodynamic optimization. The portfolio selection problem is formulated as a biconvex optimization problem with a variable weight in the Markowitz risk–return framework. In addition, the cardinality-constrained portfolio selection problem is formulated as a mixed-integer optimization problem and reformulated as a biconvex optimization problem. A two-timescale duplex neurodynamic approach is customized and applied for solving the reformulated portfolio optimization problem. In the two-timescale duplex neurodynamic approach, two recurrent neural networks operating at two timescales are employed for local searches, and their neuronal states are reinitialized upon local convergence using a particle swarm optimization rule to escape from local optima toward global ones. Experimental results on four datasets of world stock markets are elaborated to demonstrate the superior performance of the neurodynamic optimization approach to three baselines in terms of two major risk-adjusted performance criteria and portfolio returns.