Application Of Grey Multi-objective Optimization Model On Portfolio

With flourishing and maturing of stock market increasingly, more and more people take part in the securities investment. In the actual securities investment, how to estimate the income and the risk effectively, and how to seek a balance point between them, namely the best investment portfolio fitting the investor, are focuses within this domain all the time. So far, there are many results about the measure of the income and the risk of securities, but they have their own stress respectively, do not have the uniform model in theory. In addition, the majority of researches are based on massive historical data and complex process, so that actual operation is very complicated.In order to enhance feasibility of portfolio theory, this paper expresses the income and the risk with grey interval considering the complexity and the uncertainty of securities price, on the base of the elementary theories of portfolio and grey system. Then, we determine the scope of effective frontier by establishing the grey multi-objective optimization model. Thus, the investor can choose the best portfolio fitting himself from all possible situations of income - risk combination. The paper divides into five chapters as follows:Chapter 1 introduces the background,goal,meaning and the related theories about portfolio and grey system simply.Chapter 2 mainly presents several multi-objective programming models and algorithms of grey system and portfolio, and the general form of grey multi-objective programming model.Chapter 3 studies a combination forecasting method for rates of return on risky securities. First, we select plate indexes of the stock as influent factors of the stock returns, then pretreat them; Next, we choose major effect factors by grey relational analysis, forecast the securities income by establishing GM (0, N) and GM (1, 1) which are set up considering that multi-factor affect returns and its own factor does respectively. Finally, we prove this method by the actual example.Chapter 4 ascertains the best portfolio for the investor by establishing grey multi-objective optimization model. First, we obtain the grey plane of rates of return on risky securities using the curve envelope technique. So securities returns can be expressed as a grey interval. Next, we give some methods that measure risk of portfolio, then establish risk measure model with absolute-deviation based on grey number. Finally, we set up grey multi-objective optimization model, and give two solutions.Chapter 5 mainly settles the actual problem in securities investment using the grey multi-objective optimization model. The primary data are attained from weekly closing quotation of 5 stocks within three months in Chinese stock market, and then we examine the model which proposed in the 4th chapter.