Uncertain mean-chance model for portfolio selection with multiplicative background risk

Abstract

Theoretical and empirical studies all show that there are many situations where we cannot treat the indeterminate quantities as random variables. Then we need to explore using a new tool other than probability theory to make investment decisions. Using uncertainty theory, this paper discusses a portfolio selection problem considering inflation, a most popular multiplicative background risk, in such situations, and analyses the effect of uncertain inflation on investment in risky and risk-free assets. Treating risky asset return and inflation rate as uncertain variables rather than random variables, we first propose an uncertain mean-chance model. Then we give its deterministic form and compare the model with the one that ignores inflation. Next, we provide the optimal solution, which can advise the investors on how to allocate capital between risky and risk-free assets under the influence of uncertain inflation. Then by discussing the properties of the model when the return of risky asset and inflation rate obey linear uncertainty distributions, we show how the optimal investment proportion changes when the inflation rate and risky asset return change. The experiment results show that the proposed method brings investors greater wealth than the existing method using probability theory.

Keywords:

• Portfolio selection
• uncertain variables
• inflation
• multiplicative background risk
• mean-chance model

Disclosure statement

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

Data availability statement

Data sharing not applicable – no new data generated.

Additional information

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 Bachelor degree of Engineering and Master degree of Management from University of Science and Technology Beijing, her Bachelor 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 interests include portfolio selection, international investment, and investment optimization. From 2014 to 2021, she was listed in the ‘Chinese Most Cited Researchers’ published by Elsevier for eight consecutive years.

Di Ma

Di Ma, is currently working toward the Ph.D. degree of Management Science and Engineering in the School of Economics and Management, University of Science and Technology Beijing. She got her Master degree of Finance from University of Science and Technology Beijing, Beijing, China, in 2019, and got her Bachelor degree of Economics from University of Science and Technology Beijing, Beijing, China, in 2016. Her current research interests include portfolio selection, international investment, and investment optimization.