Uncertain mean–variance portfolio model with inflation taking linear uncertainty distributions

Empirical studies show that in reality there are cases where distributions obtained from past data are not close to real frequencies, which implies that we cannot treat those indeterminate quantities as random variables. In this paper, we study a portfolio investment problem with a popular multiplicative background risk, i.e., inflation, in such cases. Treating risky asset return and inflation rate as uncertain variables, we propose an uncertain mean–variance model. Then we show by analysis that when the risky asset and uncertain inflation take linear uncertainty distributions, uncertain inflation increases the investment risk and leads the investors to invest less in risky asset. Furthermore, we prove that the investment proportion of risky asset increases with the mean of inflation rate and decreases with the increase of the width of inflation rate. Finally, we provide a case analysis to show the effect of uncertain inflation on portfolio investment and the robustness of the results.