Uncertain random mean–variance–skewness models for the portfolio optimization problem

Abstract

In the face of complex financial phenomena, describing the high uncertainties in financial markets remains a challenging issue in modelling and decision making. In this paper, chance theory is used to analyse the hybrid uncertainty that combines random returns and uncertain returns. We regard the total return as an uncertain random variable and study the uncertain random portfolio optimization problem. We first define the skewness of an uncertain random variable and derive some important properties and explicit expressions with deterministic distributions. These theoretical results help transform the model into a deterministic form. Then, uncertain random mean–variance–skewness portfolio optimization models and their corresponding equivalents are established to meet the diverse needs of investors. Finally, we provide two numerical experiments to illustrate the applicability of the proposed model, one of which demonstrates that the model can be applied in the area of energy finance. It is shown that when uncertain asset returns are asymmetric, this model can be used to make investment decisions for investors. We also find that a higher return is accompanied by higher risk and higher skewness.

KEYWORDS:

• Portfolio optimization
• uncertain random variable
• chance theory
• mean–variance–skewness model
• uncertain programming

2010 Mathematics subject classifications:

• 90C90
• 91G10

Acknowledgements

This work was supported by Beijing Natural Science Foundation (grant number 9204024).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Beijing Natural Science Foundation [grant number 9204024].