Study On Cultural Algorithms And Their Applications To Portfolio Selection

This paper first gives a deep analysis on characteristics of existing evolutionary algorithms, then uses the concept of social or cultural evolution theory in social science for reference, and finally describes a series of novel algorithms, namely cultural algorithms. Cultural algorithms are dual inheritance systems based on knowledge that consist of a population space and a belief space. The population space consists of individuals. The problem solving experience of individuals selected from the population space is used to generate problem solving knowledge that resides in the belief space. Cultural algorithms utilize some characteristics and knowledge from population in the pending problems for restraining the degenerative phenomena during evolution process, so as to improve the algorithmic efficiency. Cultural algorithms are optimal algorithms in essence. Therefore, they can be used in some fields, such as cybernation, pattern recognition, optimal design, economics, etc. This paper first attempts to portfolio selection in economics.Based on researching the status quo of cultural algorithms theories and modern portfolio theory, this paper can be summarized as follows:Firstly, this paper describes the computational framework of cultural algorithms and designs its population space, belief space and all functions. Then two different versions of cultural algorithms are produced. Because most problems can be converted to nonlinear optimization problems in practice, this paper researches on how to solve this kind of problems by cultural algorithms and tests the performance of cultural algorithms. The computational experiment shows that cultural algorithms can produce substantial performance improvements. Although different type of problems has different effect, generally speaking, both versions can product the best performances.Secondly, after introducing traditional portfolio selection theory and its disadvantage, this paper expounds production and development of modern portfolio theory. Then as representation of modern portfolio theory - Markowitz's portfolio selection theory, its basal theory, conceptions and how to disperse risk are focused on.Thirdly, based on Markowitz's portfolio selection theory, a simple target portfolio investment model with different risk preference is proposed. Because some algorithms hardly get the best result for this kind model, the paper attempts to apply cultural algorithms into portfolio selection theory and propose portfolio strategies based on cultural algorithms. The results of computer simulation verify the efficiency of the proposed methods with high convergence rate.Finally, evolutionary programming which is the representation of evolutionary algorithms compares with other evolutionary algorithms. The computational experiment shows that both of versions of cultural algorithms can converge steadily and globally at higher speed. That is because cultural algorithm with dual evolutionary levels guides the search process for best solution with experience knowledge obtained from evolution process.