In real portfolio selection, the investor usually exhibits some psychological behaviors such as reference dependence, loss aversion and so on and also has the requirements of wealth expectation in his/her mental accounts, but the in-depth study on this aspect is still lacking. The objective of this paper is to develop a method for the portfolio selection in which the multiple psychological behaviors (i.e., the reference dependence, the probability overestimation or underestimation, the loss aversion and the diminishing sensitivity) and the mental accounts of the investor are considered simultaneously. First, for the multiple psychological behaviors of the investor, the calculation formula of overall comprehensive utility of portfolio of all the candidate assets is given according to the cumulative prospect theory. Then, a portfolio optimization model with the probabilistic constraints is constructed to determine the desirable portfolio. For the model, the objective is to maximize the overall comprehensive utility of portfolio of the assets, and the requirements of the wealth expectations in the mental accounts of the investor and the limitation of initial investment wealth are considered as the constraints. Further, the definition of the available state set is given, and the available state sets for each mental account can be determined according to the definition. Based on the determined available state sets, the model can be converted into the multiple linear integer programming problems. By solving the linear integer programming problems, the optimal portfolio can be obtained. In addition, a numerical example is used to illustrate the use of the proposed method. Finally, an empirical study is given to validate our research work.
A Novel Alternative Algorithm for Solving Linear Integer Programming Problems with Four Variables