Portfolio Model And Efficient Algorithm

For the varied security market, one of the most effective approaches to avoiding risk and getting the most profit is to implement portfolio investment. The modern financial theory has provided a scientific foundation and a numerical analysis method for portfolio investment. In this paper, the main work to construct some practical portfolio models and establish global convergence theories for the solution algorithms. In particular, we emphasize on the efficiency of algorithms in application compared with the existing algorithms. The major innovation is as follows:(1) A bi-objectives portfolio investment model is formulated as a single-objective one by weighting the tradeoff. Then we design penalty algorithm based on conjugate gradient method to solve it, and give global convergence theories. These ideas are applied to China stock market.(2) In order to cope with difficulties in numerical calculation caused by large penalty parameter when using non-exact penalty function, we propose a class of feasible direction algorithm. Numerical experiments have been show that this algorithm is efficient and promising in the practice.(3) Aiming at improving the practicability of Markowitz mean-variance model, we have considered transaction costs and added a random constraint. An effective solving method is designed, and numerical results are reported.