The Non-smooth Theory And Algorithm For The Optimal Solution Of Portfolio Selection

Portfolio theory is one of the problems studied by modern ?nance. In 1952,the Mean-Variance theory ?rst proposed by American economist Harry M.Markowitz.It is the basis of portfolio theory. With the development of research, several re-searchers found the factors such as transaction costs and tax has a direct impacton the behavior of investors. Therefore people focused on the portfolio selectionwith transaction costs. Because of nondi?erential of transaction costs function,the traditional method is that we transform the nondi?erential model into a dif-ferential model. The solution of the new problem is the solution of the old one.Butthis method is complicated. We hope an easier one.This paper studied the portfolio model with transaction costs. Based onlinear weighted sum method, the multi-objective optimization problem is trans-formed into a Single objective optimization problem, then we analysis the opti-mal solution. The nondi?erential of transaction costs function brings trouble, webring into subdi?erential, according to the de?nition, we solve the subdi?erentialof transaction costs function, and we prove it. According to K-T condition andFritz-John condition, we give the algorithm. For testing the e?ectiveness of thealgorithm, we use the data of the paper [29], and compared the results. It isproved that the algorithm is e?ective, and sometimes is better than the former.