Mean-Variance-Skewness-Kurtosis Optimization Portfolio Selection Model in Uncertain Random Environments

Abstract

The main focus of this paper is to address the computational challenges associated with portfolio optimization in a hybrid uncertainty (Uncertain-Random) environment. Considering the fact that investors consider different subjective criteria for choosing their portfolio, in this research in presenting the models, we have used different criteria such as skewness and kurtosis of the distribution of stock return variables, which can be very effective in investors’ decision-making.
The paper assumes that the total return can be characterized as a hybrid uncertain variable and investigates the problem of optimal portfolio selection under uncertain randomness.
The initial step involves defining the skewness and kurtosis of ncertain random variables, followed by the derivation of several important properties in specific distributions. These findings enable the transformation of models into deterministic forms and the establishment of uncertain random mean-variance-skewness-kurtosis optimization models for portfolio selection, thereby eliminating the need for investors to make subjective decisions.

Furthermore, the paper proposes the use of a capable artificial neural network that is globally convergent and stable to solve the obtained model. A neumerical simulation result demonstrates the efficiency of the neural network in solving the portfolio optimization problem. The work done can be applied to solve real-life portfolio selection problems with better accuracy.