Research on Stock Market Portfolio Optimization Using Stochastic Matrix Theory and Genetic Algorithm

Abstract

Financial engineering is a synthesis of modern finance, information technology, engineering, and other fields. Under the complex and volatile market conditions, how to allocate assets reasonably to minimize the benefits and risks assumed is a very important topic. Using the principle of random matrix, the correlation statistical characteristics of stocks are analyzed, the noise reduction and reconstruction algorithm of the correlation matrix is discussed, and a new noise reduction algorithm, two-point determination method, is given. The investment portfolio is numerically simulated, and its parameters are set by the orthogonal experimental method. Through analysis, it is found that the eigenvector contained in the maximum eigenvalue of the correlation matrix can be regarded as a market indicator. The “two-point determination method” has a good effect in “denoising” and can provide operational decision-making and technical support for portfolios.