Uncertain Mean Absolute Deviation Portfolio Decisions-making With Real Constraints

To deal with subjective uncertainty,the paper used the uncertainty mean and the uncertainty absolute deviation to measure the return rate and risk of risk assets based on the uncertainty theory.Taking into account the linear constraints(return,risk,transaction cost,upper and lower limits of investment ratio,borrowing constraints,restrictions on short selling),entropy constraints,minimum transaction lots restrictions and multi-period investment,the paper constructed an uncertain mean absolute deviation portfolio decision model with real constraints and analyzed the influence of different constraints on portfolio decision.Firstly,on the basis of linear constraints,Shannon entropy,Yager entropy and linear proportional entropy were introduced respectively to construct three different entropy constraint portfolio decision models.The three models was solved by using sequence linear programming combined with rotation algorithm and the most suitable entropy constraint model was selected through empirical comparison.Then,on the basis of entropy constraint,a portfolio decision model with minimum transaction lots restrictions was constructed.The mixed integer programming of CPLEX software was used to solve the model,and the sensitivity of various constraints was analyzed through the sample data.Finally,the above single-period investment is extended to multi-period investment,and a multi-period portfolio decision model with real constraints was constructed.The multi-period model was transformed into multiple submodels according to time,and the mixed integer programming of CPLEX software was used to solve the submodels.The out of sample data was used to analyze the sensitivity of each constraint so as to verify the effectiveness of the model and algorithm.The results showed that :(1)the portfolio model with Yager entropy constraint can not only satisfy the portfolio diversity and high sharpe ratio,but also not affect the portfolio adjustment.(2)When the maximum borrowing decreases,the upper limit of the risk assets investment proportion increases,the pre-determined entropy value decreases,and the pre-determined rate of return decreases,it caused the increase of the investment proportion of risk-free assets—the decrease of the sum of the investment proportion of risky assets—which lead to the reduction of transaction cost,risk,the number of risky assets and the increase of sharpe ratio.(3)After increasing the minimum transaction lots restrictions,the investment proportion of risk-free assets increased,the risk increased and the sharpe ratio decreased.(4)When the maximum borrowing decreases,the upper limit of the risk assets investment proportion increases,the pre-determined entropy value decreases,and the pre-determined rate of return decreases,the systematic risk of multi-period investment portfolio decreased.However,no matter how the constraint conditions change,the real wealth of the portfolio in each period was basically greater than the real wealth of the SZ180,which showed the effectiveness of the model and algorithm.