Research On Improvement And Application Of Multi-objective Mean-variance Model In Portfolio Problem

With the development of China’s economy, more and more Chinese have realized that investment plays an important role. Therefore, for the investors, how to allocate the capital to a set of assets for higher gain and lower risk is the chief problem, which is also the key of portfolio problem. The theory of portfolio was proposed in the 1950 s by Markowitz, which laid the foundation of the subsequent study.Therefore, in order to obtain a model which can be more suitable for Chinese market and provide the investors with reasonable portfolios by scientific method to improve the efficiency of solving the portfolio problem, in this paper, on the basis of the classical Mean-Variance Model, combining with present situation and the characteristics of investors of Chinese investment market, we mainly do following research:Firstly, some research is done on the hypothesis of the Mean-Variance Model. On this basis, through the way of adding constraints, an improved model is established which involves transaction cost and risk-free asset to obtain a model more in line with Chinese investment market. What’s more, derived models are introduced to meet different requirements of different investors when the investors don’t consider transaction cost and risk-free asset or only consider one of transaction cost and risk-free asset.Secondly, in order to obtain portfolios which belong to Pareto set, H-PBIL is designed on the basis of PBIL(Population-Based Incremental Learning, PBIL), combining fast non-dominated sorting mechanism and crowding distance of NSGA-II(Nondominated Sorting Genetic Algorithm-II, NSGA-II). Meanwhile, improved histograms are also applied in this algorithm. As a result, the population of portfolios will converge to the Pareto front and the investors can get the Pareto set. Moreover, in order to test the effectiveness of H-PBIL, the convergence performance and diversity performance as well as computational efficiency of the Pareto front are tested by the data in OR-Library. Meanwhile, we also compare the solutions of H-PBIL and NSGA-II to prove the effectiveness of the approach. On this basis, we solve the four kinds of models by the algorithm proposed in this paper, and the validity of the models is confirmed.Finally, a decision process is designed to assist investors in choosing favorite investment plan and realize the effective application of the models. And in the application, we apply the four models with the actual data in Shanghai and Shenzhen A-shares main board market. Investors are able to choose their prefer model through the decision process. What’s more, it’s also easy to choose their favorite portfolio from Pareto set with the help of this process. In this way, not only the burden of investors is reduced, but also the application value of the portfolios in the Pareto set is also improved.