Differential Evolution Algorithm And Its Application In Finance Portfolio Optimization

In recent years, a new evolution algorithm which called Differential Evolution Algorithm (DE) has captured the scholars'attentions. The main features of DE are simple to use, fast convergence speed and few field knowledge needed. Through massive researches, we found that DE has very strong restraining ability and it is more suitable to solve some complex optimization problems.DE has obtained many research results. Compares with other evolution algorithms, it is more effective to solve optimization problems. However, it also has some threats to improve, because that DE has not been matured yet both in theory and in practice. Therefore, DE should be kept on researching to expend the application area and solve more problems.Theory of portfolio optimization is an important part of the modern finance investment theories to discuss the investment rules of finance market and offer theoretic guide for investors. It had done that through using mathematical facilities such as convex analysis, random analysis, non smooth analysis, (nonlinear) programming etc, combining with the basic method of modern portfolio theory- the mean-variance method and establishing mathematical models. This paper is mainly focused on following aspects:(1)Analyze the important meanings of DE. Additionally, the principle of DE will be introduced minutely, and some related questions about DE will be researched systematically such as the change form of algorithm, the data structure, the establishment of parameter, the corrective method, the main feature and its applications.(2)Based on the in-depth study of dissipative structure theory, the introduction of the dissipative structure theory to analyze the differential evolution algorithm, while the success of individual variation and crossover between the number of links, so that individual variations influence the success of crossover operator will improve the basic differential evolution algorithm with crossover and mutation for the adaptive differential evolution algorithm, and experimental results verify the improved algorithm has strong global convergence and robustness.(3)Outline the characteristics of financial products, the basic concept of portfolio theory and the optimization problem of financial products portfolio. And also, I made a detailed description of the traditional mean– variance model, establish a new portfolio model, apply the standard differential evolution algorithm there and prove the effectiveness of the algorithm and the correctness of model. Moreover, compared with Particle Swarm Optimization (PSO) and DE under the same risk factors to prove DE is the efficient and reliable combinatorial optimization in this kind of optimal combination.(4)Used improved algorithm to optimize the standard Markowitz model, to enrich and perfect the technology and theory of the Economic optimization method. Furthermore, find out the minimum risk of the financial product portfolio efficiently on the premise of solving a given expected rate of return, in order to provide a reasonable investment plan to the investors.