The Optimizational Stock Portfolio Investment Model And Its Effective Solving Method

With the growing comprehensive national power of China,people's living standards rising,people's income increases and the enhancing awareness of people's investment.Investor use their surplus money into the stock market,so China's stock market is increasing more attention.Chinese investors from the beginning of blind investment and follow the "inside story"to the present become more and more rational,more attention to the knowledge of the technical.Economics consider the greater the income,the greater the risk.But in the face of the vagaries of the stock market, investors concerned about the profit, but more concerned about the risks, investors want to get the balance of benefits and risks.The portfolio investment is the most effective approaches to avoiding risk and getting the most profit.The portfolio management objective is to achieve the maximum benefits on investment,and to make the portfolio of risk and benefits characteristics to bring to the satisfaction of investors. Markowitz,a famous American economist,created the modern portfolio theory through the benefits and risks of quantitative description, opening a new chapter in portfolio theory.Markowitz model assumptions are too idealistic,so it is difficult to reflect current stock market.Moreover China as a developing country, with Chinese characteristics under the conditions of the socialist market economy, the stock market is still a weak efficient market, this makes Markowitz model application in stock market always existsa series of problems. In this paper,based on the portfolio model and the market in our country's actuality,the practicality of the model were improved, hope to the investors in stock market has helped.This paper describes the mathematical description of the Markowitz model at first,on this basis put forward a practical model for portfolio investment.Because of model's features,we use outside point penalty algorithm and established the global convergence theories.At last a numerical example explained the effection to solve the practical problems.In this paper,the main innovations are as follows: in the portfolio model to consider the worst benefits, and use of preference factor will double objective optimization problem into single objective problem, according to the characteristics of optimization problems,used outside the penalty function method and the conjugate direction method for iterative search.