Study On The Problem Of Fuzzy Portfolio

Abstract:Optimal portfolio problem has always been one of the core problems of the financial research. Since there are many uncertain factors in the real securities market, the research of portfolio problem under the fuzzy environment makes more sense. The risk analysis in the traditional fuzzy portfolio problem only consider the portfolio risks arising from the portfolio investment, ignoring the background risk generated outside the portfolio. Considering the presence of background risk has a great influence on the decision-making behavior of investors, this article will introduce the background risk to the fuzzy portfolio.First of all, this paper analyzes the portfolio selection model considering the background risk, while the securities return are seen as fuzzy variables under fuzzy environment. A study is carried out using the data from some stocks, we get the efficient frontier of the fuzzy portfolio with the background risk, and compare with the efficient frontier of portfolio without background risk. A conclusion is researched that considering background risk can reflect the investment risk of the real economy environment and make the investors choose a portfolio more suitable to them.In addition, the membership function of the normal fuzzy number from minus infinity to plus infinity, but in fact the return of the risk assets must be in a limited range. Therefore,it is not appropriate to use the normal fuzzy number describing the return of the risk assets. In order to better describe the return of the risk assets, this paper constructs a symmetric triangular fuzzy number, which not only keeps the mean and variance of the normal fuzzy number, but also has the nature of the triangular fuzzy number, so it can better reflect on the distribution of the risk assets return. Finally, we introduce the new form of the fuzzy membership function into the fuzzy portfolio model, the solution of this optimal portfolio contains more information.