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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.

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