Multi-period Portfolio Optimization Model About Fuzzy Variables

Taking into account the risk of diversification,people usually choose a variety of investment projects;in order to make the proportion of investment more appropriate also need to diversify the allocation of specific investment assets,with this problem,resulting in a portfolio theory.While the public behavior in the investment market is affected by many factors such as thinking and environment,the ambiguity of judge by people and the complexity of the economic phenomena make financial markets behave uncertainly and ambiguously.For this reason,the traditional probability theory method for portfolio model can't meet the needs from the real market,rational investment decision-making to meet the risk-benefit balance at the same time also need to consider many criteria.Therefore,the fuzzy method is more suitable than the probability method to express the real financial market uncertainty.Based on the classical mean variance theory,the concept and the possibility theory of fuzzy sets,this paper uses the fuzzy method to express the uncertainty in the financial market.Under the premise of satisfying the maximum profit and the minimum risk of the investor,assuming that the yield is a fuzzy variable,and the corresponding fuzzy portfolio optimization model is obtained.Because the investment market in real life is complex and mobile,we also consider many other factors while satisfying the equilibrium of risk and return,for example:the transaction cost,the degree of diversification,etc.For the case that the asset has the same investment term,the fuzzy investment portfolio optimization model is established under the assumption that the yield is a fuzzy variable,taking into account the factors of the movement market.Under the condition that the yield rate is the linear combination fuzzy variable of historical rate of return,the corresponding fuzzy portfolio optimization model is established,and all the examples are verified,compared with the traditional model results,more in line with the reality of the financial market situation.For the case where the asset has different investment term,it is assumed that the investment term of the asset may be less than the investment period or may be greater than the investment period,and the corresponding wealth expression is obtained respectively,and give the corresponding example verification.