Research On Portfolio Model And Its Algorithm

Theory of portfolio optimization is an important part of the modern finance investment theories. Which uses mathematical facilities such as convex analysis, random analysis, nonsmooth analysis, nonlinear programming etc, combined with the mean-variance method—the basic method of modern portfolio theory. By setting up mathematical models, discussed the investment rules of finance market and offers theoretic guide for investors. The main results of the thesis can be summarized as follows:◆ Several basic portfolio models have been summarized firstly;◆ Considering the real market conditions, Chance-dependence model and Goal-programming model with transaction costs as well as no short sales is developed for optimal portfolio selection and the dynamic rules with transaction costs rate changing is analyzed;◆ Secondly the problem of portfolios in uncertainty environment is investigated .The mathematical model for the portfolio selection is established by credibility distribution rather than possibility or probability distribution. We present a hybrid intelligent algorithm for finding an approximate optimal solution which to satisfy investor's aspiration (in the sense of utility scores) to the n-asset portfolio selection problem under credibility distribution. We give an example to show the efficiency of our method.◆ The question of portfolio selecting is investigated in the fuzzy environment. In our model, the fuzzy variable is introduced. We give not only the crisp optimal solution but also some regions of potential satisfactory solution around the optimal solution...