THE SPARSE PORTFOLIO OPTIMIZATION WITH STOCHASTIC DOMINANCE AND BACKGROUND RISK AND THE SLQPSO ALGORITHM

Abstract

In this paper, we propose a new sparse portfolio optimization model involving stochastic dominance and background risk (SPSDBR). This model caters to the needs of risk-averse groups who can only invest in a limited number of assets in real life. Due to the presence of random variables in the model, we provide a sample average approximation (SAA) method to approximate the new model and give the results of asymptotic convergence. Additionally, due to the non-convex and non-smooth nature of the new model, we propose an improved quantum-behaved particle swarm optimization algorithm with S-shaped function and a Lévy flight (SLQPSO) to solve it. The algorithm combines an S-shaped function and a Lévy flight mechanism which can enhance the the particle’s exploration ability and broaden the range of particle search at the same time. We tested 11 classic benchmark functions, and the SLQPSO algorithm demonstrated superior performance compared to six existing metaheuristic algorithms. Furthermore, the proposed SLQPSO algorithm also shows good performance in solving SPSDBR models with and without transaction cost functions under different market conditions, achieving better convergence and robustness compared to other algorithms. The SPSDBR model effectively captures the impact of background risk, sparsity level, and transaction costs on portfolio optimization, providing practical insights for investors.