The Design And Implementation Of Improved PSO Algorithms For Portfolio Optimization

The key problem of financial investment is a trade-off between risk and return. To solve the problem, Markowitz proposed the mean-variance model (M-V model) which provided a quantitative framework for portfolio selection, establishing the foundation of modern portfolio selection theory. The portfolio selection problem proved to be a typical NP-hard problem for which no computational efficient algorithms have been proposed. Particle swarm optimization is a collaborative population-based meta-heuristic algorithm and has proven effective in many empirical studies. There has been some researches introducing PSO into portfolio optimization problems, but few of them lay an emphasis on the improvement of the performance for PSO when applied to this specific problem. In this paper, we introduce PSO algorithm for solving portfolio optimization problems. We propose a PSO algorithm based on Heterogeneous Multiple Population Strategy and a PSO algorithm based on Random Population Topology Strategy according to the characteristics of the problem. In addition, we conduct some empirical researches for M-V model in the Chinese securities market. The main content of this paper is as follows:1) Proposing an improved PSO algorithm——HMPPSO based on the strategy of Heterogeneous Multi-ple Population to solve a generalized M-V model which considers cardinality constraints and bound-ing constrains. In the proposed strategy, the whole population is divided into several sub-populations and each sub-population evolves separately with a different PSO variant. These sub-populations share information regularly, using the different capability of exploration and exploitation during the process of evolution to help improve the performance of the whole population. The proposed HMPPSO was tested on benchmark datasets for portfolio optimization problems and compared with other classic PSO variants. Experiments show that HMPPSO is much effective and robust, especially for problems with high dimensions, which verifys the effectiveness of the proposed Heterogeneous Multiple Population Strategy.2) Proposing four improved PSO algorithms (RTWPSO-AD, RTWPSO-D, DRWTPSO-AD, DRWTPSO-D) based on the strategies of Random Population Topology. Adopting the Random Population Topology Strategy, the topology of PSO is abstracted into an undirected connected graph and can be generated randomly according to a predetermined degree. The computational results demonstrate that the popu-lation topologies of PSO have direct impacts on the information sharing among particles, thus improve the performance of PSO obviously. In particular, the proposed DRTPSO-D shows an extraordinary per-formance in most test data set, providing an effective solution for the portfolio optimization problem.3) Proving the effectiveness of M-V model in the Chinese securities market, testing its risk decentraliza-tion effect as well as proposing a M-V-S model which considers systemic risk. First, the proposed algorithm HMPPSO is adopted to solve a generalized M-V model and three methods for parameter estimation is compared. Then the systemic risk is introduced into the M-V model and the time series of stock index return under different value of systemic risk parameter is compared. The experiments demonstrate that the portfolio obtained based on M-V model can diversify risk effectively with a small-er fluctuation of return than the Shanghai Composite Index. The M-V-S model can diversify the total risk of portfolio to some degree, especially when the prices of stocks is in a steady condition, thus can provide a more robust investment decision for investors.In this paper, a PSO algorithm based on Heterogeneous Multiple Population Strategy and a PSO algo-rithm based on Random Population Topology Strategy are proposed for the portfolio optimization problem and have achieved good performance. The work conducted in this paper can provide gist for the application of intelligence algorithms in the field of portfolio optimization. What’s more, it can provide complement to the application of M-V model in the Chinese securities market with important theoretical and practical significance.