Order υ Entropy and Cross Entropy of Uncertain Variables for Portfolio Selection

PurposeThe reported Kullback–Leibler (K–L) distance-based generalized grey target decision method (GGTDM) for mixed attributes is an asymmetric decision-making basis (DMB) that does not have the symmetric characteristic of distance in common sense, which may affect the decision-making result. To overcome the deficiency of the asymmetric K–L distance, the symmetric K–L distance is investigated to act as the DMB of GGTDM for mixed attributes.Design/methodology/approachThe decision-making steps of the proposed approach are as follows: First, all mixed attribute values are transformed into binary connection numbers, and the target centre indices of all attributes are determined. Second, all the binary connection numbers (including the target centre indices) are divided into deterministic and uncertain terms and converted into two-tuple (determinacy and uncertainty) numbers. Third, the comprehensive weighted symmetric K–L distance can be computed, as can the alternative index of normalized two-tuple (deterministic degree and uncertainty degree) number and that of the target centre. Finally, the decision-making is made by the comprehensive weighted symmetric K–L distance according to the rule that the smaller the value, the better the alternative.FindingsThe case study verifies the proposed approach with its sufficient theoretical basis for decision-making and reflects the preferences of decision-makers to address the uncertainty of an uncertain number.Originality/valueThis work compares the single-direction-based K–L distance to the symmetric one and uses the symmetric K–L distance as the DMB of GGTDM. At the same time, different coefficients are assigned to an uncertain number’s deterministic term and uncertain term in the calculation process, as this reflects the preference of the decision-maker.

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

Deng

Huang

2021

IFS

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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.

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Order υ Entropy and Cross Entropy of Uncertain Variables for Portfolio Selection

Cited by 4 publications

References 23 publications

Renyi entropy of uncertain random variables and its application to portfolio selection

Renyi entropy of uncertain random variables and its application to portfolio selection

Symmetric Kullback–Leibler distance based generalized grey target decision method for mixed attributes

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

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