Characterizing compromise solutions for investors with uncertain risk preferences

Abstract

The optimum portfolio selection for an investor with particular preferences was proven to lie on the normalized efficient frontier between two bounds defined by the Ballestero (1998) bounding theorem. A deeper understanding is possible if the decision-maker is provided with visual and quantitative techniques. Here, we derive useful insights as a way to support investor's decision-making through: (i) a new theorem to assess balance of solutions; (ii) a procedure and a new plot to deal with discrete efficient frontiers and uncertain risk preferences; and (iii) two quality metrics useful to predict long-run performance of investors.

Geometric compromise programming: application in portfolio selection

“…These empirical results agree with other theoretical results presented by Ballestero (2007) and Salas‐Molina et al. (2019) in the same context of portfolio selection. These results can be summarised as follows: the larger the value of p in Zeleny–Yu utility $$U_{\text{ZY}}$$ from Equation (5), the more balance is achieved by recommended portfolios or, in other words, the further the portfolios from corner solutions.…”

“…When considering vector of weights w in Zeleny–Yu utility in Equation (5), we find two different approaches in the literature. In CP, we usually find weights raised to metric p (see, e.g., Ballestero and Romero, 1996; Salas‐Molina et al., 2019). This course of action results in the following weighted multiplicative function as shown in the Appendix: $$$$\begin{equation} \lim _{p \rightarrow 0} {\left[ \sum _{j=1}^q w_j^p z_j^p \right]}^{(1/p)} = {\left[ \prod _{j=1}^q w_j z_j \right]}^{(1/q)}.$$…”

“…Salas‐Molina et al. (2019) proposed different practical tools to deal with discrete efficient frontiers and uncertain risk preferences for cases $$p=1$$ and $$p=2$$. Caçador et al.…”

Non-linear Neutrosophic Numbers and Its Application to Multiple Criteria Performance Assessment

“…In other works, the order of non-linearity is used either as an expression of ethical principles [36,37], or as indicative of the balance of solutions [38,39]. We here follow the approach of using the order of non-linearity as an expression of the uncertainty, hence providing more flexibility to decision-makers.…”

Shared value economics: an axiomatic approach

“…Note also that the area under curve z (E, B) is higher than the area under curve z(E, B). Adapting the recommendations in Salas-Molina et al (2017) to our context, we propose the following quantitative definition of shared value creation.…”