Optimal portfolio selection based on satisfaction index

In this paper, optimal portfolio selection with uncertain returns is studied, and corresponding model based on the satisfaction index is proposed. In the model, the risk is taken as the sum of the absolute deviation of the risky assets in stead of covariance, the transaction cost is taken as v-shaped function of the difference between the existing and new portfolio. An efficient way is given to transform a non-linear problem into a linear problem, which alleviate the computational difficulty greatly. Numerical result showed that the proposed method is capable of helping investor to find efficient portfolios according to his/her preference.