A Study on Improved Particle Swarm Optimization Algorithm in Portfolio Optimization Problem

The PSO algorithm suffers from a singular population and a propensity to settle on a local optimal solution. We propose CPSO algorithm to enhance the diversity of the particle population and prevent local optima. The algorithm modifies the initialization process to ensure higher diversity and ergodicity of particles within the pre-stage. It employs non-linearly varying inertia weights and acceleration coefficients and introduces the Cauchy variational operator to increase population diversity and prevent particles from becoming trapped in local optima. According to the experimental findings, it shows that the CPSO algorithm has improved precision in terms of convergence and a faster rate of convergence for optimization problems of high complexity. It can achieve higher Sharpe ratios in the portfolio optimization problems.

I. Introduction

As the Chinese stock market experiences exponential growth, more and more people are choosing to invest their capital in the stock market for high returns. However, stock investment is a highly volatile, high-risk, high-return investment. Lack of investment concepts or improper investment methods can cause investors to lose their principal. Portfolio optimization refers to the construction of investment Portfolio optimization involves the strategic construction of investment portfolios and the utilization of optimization algorithms. These tools assist investors in formulating the most advantageous asset allocation strategy across various investment products. This approach serves to diversify investment risks effectively while aiming to maximize investment returns. Consequently, portfolio optimization has emerged as a compelling and vital area of focus within contemporary investment theory.