Cardinality Constrained Portfolio Optimization Using a Hybrid Approach Based on Particle Swarm Optimization and Hopfield Neural Network

摘要

Portfolios are an appropriate mix or collection of investments held by an institution or an individual. The Portfolio optimization is an important field in financial science. It determines the optimal capital weightings for a basket of investments so as to give the highest return and the least risk for investors. This paper investigates a portfolio optimization problem with some constraints like boundary and cardinality which are more appropriate for real world conditions. The problem is formulated as a mixed integer quadratic programming model for which exact methods cannot find the optimal solution efficiently. In order to trace out the efficient Frontier, we consider a Hopfield neural network (HNN), and hybridize it with a particle swarm optimization (PSO) algorithm. PSO is a computationally effective optimal seeking algorithm, while HNN is a kind of recurrent artificial neural network in computer science. Various parameters of proposed algorithm are calibrated by means of a statistical method which is based on Taguchi technique. Computational results which were done on benchmark problems signify that our proposed algorithm outperforms the traditional heuristic algorithms previously presented to solve the cardinality constrained portfolio problem.