Research On Multi-stage Fuzzy Portfolio

The mean-variance model proposed by Markowitz has been the basis of modern financial theory since the 1950 s,which combines probability and optimization techniques to model investment under behavioral uncertainty.The key principle of MV model is to use the expected return of a portfolio as the investment return and the variance of a portfolio as the risk measure.After Markowitz’s research work,many subsequent portfolio optimization work has improved and expanded the standard MV Model from the following three directions:(1)simplification of type and quantity,input of data;(2)Introduction of Alternative Risk Measures;(3)incorporate real-world constraints.This paper focuses on the second and third directions.Investors want the best trade-off between return and risk.In portfolio optimization,the mean-absolute deviation model is used to minimize the return and risk.However,according to the previous research,the maximum entropy is not considered in the mean-absolute deviation model.In fact,higher entropy leads to portfolio diversification,which reduces portfolio risk.Therefore,in this paper,we propose a multi-period portfolio optimization model,namely,the mean value absolute deviation of portfolio optimization with maximum entropy.The model named as the portfolio manager entropy.In addition,the proposed model combines the optimal values of each objective function using the objective programming method.The objective function of the model is to maximize the average return,minimize the absolute deviation and maximize the entropy of the portfolio.This paper assumes that the investment environment is uncertain,that the expected return and turnover of assets are fuzzy variables with normal distribution,and uses an extension of fuzzy number,triangular fuzzy number and trapezoidal fuzzy number,using the average absolute deviation as the risk measure,the multi-stage fuzzy portfolio problem is introduced on the basis of the empirical verification of the single-period portfolio optimization model,the problem is a dynamic linear programming problem to maximize the terminal wealth under risk control.The goal of this article is to give investors more authority to specify risk tolerance and to design the best investment plan for different investment scopes.The model also includes fuzzy liquidity constraints,Yager entropy constraints,risk control,threshold constraints and transaction costs for each investment cycle to capture various stock market scenarios.Based on the theory of possibility measure,this paper uses the mean of possibility,absolute deviation,Yager entropy and fuzzy turnover rate to describe the return,risk,dispersion and liquidity of portfolio respectively,a multi-stage fuzzy portfolio optimization model with risk control,threshold constraint(short selling constraint),fuzzy liquidity constraint and Yager entropy constraint including transaction cost is proposed.The forward dynamic programming method is used to solve the result model and obtain the optimal solution of the portfolio.Finally,based on the real data of Shanghai Stock Exchange,the behavior of the model and the Algorithm designed are illustrated.The conclusions drawn from the analysis emphasize the importance of accurately assessing the current stock market outlook and adopting a correct portfolio strategy,we should consider the upper and lower bounds(threshold constraint),the Yager entropy constraint and the fuzzy liquidity constraint in real stock investment,which must be included in the portfolio optimization.