Mean-entropy uncertain portfolio with risk curve and total mental accounts under multiple background risks

Abstract

In the previous uncertain portfolio literature on background risk and mental account, only a general background risk and a few kinds of mental accounts were considered. Based on the above limitations, on the one hand, the multiple background risks are defined by linear weighting of different background asset risks in this paper; on the other hand, the total nine kinds of mental accounts are comprehensively considered. Especially, the risk curve is regarded as the risk measurement of different mental accounts for the first time. Under the framework of uncertainty theory, a novel mean-entropy portfolio model with risk curve and total mental accounts under multiple background risks is constructed. In addition, transaction fees, chance constraint, upper and lower limits and initial wealth constraints are also considered in our proposed model. In theory, the equivalent forms of the models with different uncertainty distributions (general, normal and zigzag) are presented by three theorems. Simultaneously, the corresponding concrete expressions of risk curves are obtained by another three theorems. In practice, two numerical examples verify the feasibility and effectiveness of our proposed model. Finally, we can obtain the following unique and meaningful findings: (1) investors will underestimate the potential risk if they ignore the existence of multiple background risks; (2) with the increase of the return threshold, the return of the sub-portfolio will inevitably increase, but investors also bear the risk that the risk curve is higher than the confidence curve at this time.