In classical Markowitz＇s Mean-Variance model, parameters such as the mean and covari- ance of the underlying assets＇ future return are assumed to be known exactly. However, this is not always the case. The parameter...In classical Markowitz＇s Mean-Variance model, parameters such as the mean and covari- ance of the underlying assets＇ future return are assumed to be known exactly. However, this is not always the case. The parameters often correspond to quantities that fall within a range, or can be known ambiguously at the time when investment decision must be made. In such situations, investors determine returns on investment and risks etc. and make portfolio decisions based on experience and economic wisdom. This paper tries to use the concept of interval numbers in the fuzzy set theory to extend the classical mean-variance portfolio selection model to a mean-downside semi-variance model with consideration of liquidity requirements of a bank. The semi-variance constraint is employed to control the downside risk, filling in the existing interval portfolio optimization model based on the linear semi-absolute deviation to depict the downside risk. Simulation results show that the model behaves robustly for risky assets with highest or lowest mean historical rate of return and the optimal investment proportions have good stability. This suggests that for these kinds of assets the model can reduce the risk of high deviation caused by the deviation in the decision maker＇s experience and economic wisdom.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.71301017,71731003,71671023,11301050 and 51375067the National Social Science Foundation of China under Grant No.16BTJ017+1 种基金China Postdoctoral Science Foundation Funded Project under Grant No.2016M600207the Doctoral Fund of Liaoning Province under Grant No.20131017
文摘In classical Markowitz＇s Mean-Variance model, parameters such as the mean and covari- ance of the underlying assets＇ future return are assumed to be known exactly. However, this is not always the case. The parameters often correspond to quantities that fall within a range, or can be known ambiguously at the time when investment decision must be made. In such situations, investors determine returns on investment and risks etc. and make portfolio decisions based on experience and economic wisdom. This paper tries to use the concept of interval numbers in the fuzzy set theory to extend the classical mean-variance portfolio selection model to a mean-downside semi-variance model with consideration of liquidity requirements of a bank. The semi-variance constraint is employed to control the downside risk, filling in the existing interval portfolio optimization model based on the linear semi-absolute deviation to depict the downside risk. Simulation results show that the model behaves robustly for risky assets with highest or lowest mean historical rate of return and the optimal investment proportions have good stability. This suggests that for these kinds of assets the model can reduce the risk of high deviation caused by the deviation in the decision maker＇s experience and economic wisdom.
