Uncertain portfolio selection with mental accounts

Abstract

Since the security market is so complex, in real life, there are situations where the future security returns cannot be reflected by the past data and are given by experts' estimations according to their knowledge and judgement rather than by historical data. This paper discusses a portfolio selection problem in such an uncertain environment. In the paper, in order to reflect different attitudes towards risk that vary by goal in one portfolio investment, we apply mental account to the investment. Using uncertainty theory, we propose a new mean–variance uncertain portfolio selection model with mental accounts. Furthermore, we discuss the shape of the mean–standard deviation efficient frontier of the subportfolios of each mental account when security returns are normal uncertain variables and further give the condition where the optimal aggregate portfolio is on the mean–standard deviation efficient frontier. In addition, we compare the optimal portfolio with mental accounts with that without mental accounts. Finally, a numerical example is given as an illustration.

Keywords:

• Uncertainty modelling
• portfolio selection
• uncertain variable
• uncertain programming
• mental accounts

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Social Science Foundation of China [No. 17BGL052] and the Fundamental Research Funds for the Central Universities [No. FRF-MP-20-12].

Notes on contributors

Xiaoxia Huang

Xiaoxia Huang, Ph.D., is a professor and associate dean in the School of Economics and Management, University of Science and Technology Beijing. She got her Balchelor degree of Engineering and Master degree of Management from University of Science and Technology Beijing, her Balchelor degree of Economics from University of International Business and Economics, and her Ph.D degree in Management Science and Engineering from Beijing Institute of Technology. Her major research areas include portfolio selection, international investment, and investment optimization. From 2014 to 2019, she was listed in the ‘Chinese Most Cited Researchers’ published by Elsevier for six consecutive years.

Hao Di

Hao Di received his Ph.D. degree from University of Science and Technology Beijing, Beijing, China, in 2016. From 2016 to 2018, he did postdoctoral research in Guanghua School of Management at Peking University. Currently, he is a manager of Harvest Fund Management Co., Ltd?Beijing, China. He chaired a China Postdoctoral Science Foundation project and participated in four National Natural Science Foundation projects. He is also a reviewer for journals such as Optimization, Journal of Industrial Engineering and Management Science, and Southern China Finance. His current research interests include asset allocation and risk management.