| In 1952, American economist Markowitz published an article entitled Portfolio Selection, and set up the famous portfolio selection model, which indicated that the portfolio selection transferred from qualitative research to quantitative research. Markowitz's portfolio selection model has some existent problems: all securities are perfectly divisible, non-transaction cost on single-period, without considering that investment strategies changes according to the market. Therefore, it deviates the real market, and has maneuverability difficulty.Firstly, this paper introduces the theory of portfolio selection, and expounds the advantage and disadvantage of the theory of Markowitz. Then, based on the idea of the theory of Markowitz, under risk measureβ, this paper proposes multi-period models of portfolio investment with class constraints, transaction cost and the securities which can't be divided. It considers the situations of multi-periods. When an investor joins the securities market for the first time, he or she decides portfolio investment according to the practical conditions of securities market. In addition, investors should adjust the portfolio according to market changes, and discuss the following two situations: (1) Don't change the kinds of the risky securities; (2) Change the kinds of the risky securities.The optimal portfolios are often sensitive to perturbations in the parameters of the expected returns and the covariance matrix. So, based on multi-period models of portfolio investment, the robust multi-periods models of portfolio selection are established. Then, we analyze the models, convert them to SOCP.Finally, the paper gives an illustration of the multi-period models of portfolio investment under risk measureβ. It chooses 23 stocks of Shanghai Stock Exchange to invest, and adopts the closing price of everyday in April of 2005 to compute. The paper suggests the hybrid genetic algorithm to solve the problems. The result shows that these models have a good effect. |
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