Risk Index Based Uncertain Portfolio Selection with Monotone Increasing Multiplicative Background Risk

Investors usually invest not only in risky assets but also in risk-free assets and face not only portfolio risk but also background risk. This paper discusses an uncertain portfolio selection problem in risky assets and risk-free assets with monotone increasing multiplicative background risk (MBR), which is prevalent but less research has been done. To do so, we first propose an uncertain mean-risk index model based on uncertainty theory where the security return and MBR are regarded as uncertain variables and give the deterministic form of the model. Then for further analysis, we discuss the critical constraint and optimality condition of the model. Based on the discussion, we study the influence of uncertain MBR on the investors' decisions. Finally, we provide the case analysis to illustrate the application of our method and the analysis results.