Fuzzy Portfolio Selection in the Risk Attitudes of Dimension Analysis under the Adjustable Security Proportions

Abstract

Fuzzy portfolio models have received many researchers’ focus on the issue of risk preferences. The portfolio based on guaranteed return rates has been developing and considering the dimension of excess investment for the investors in different risk preferences. However, not only excess investment but also shortage investment to the selected portfolio should be considered for risk preferences, including risk-seeking, risk-neutral, and risk-averse, by different degrees of dimensions in excess investment and shortage investment. A comparison to the degree of dimensions for the excess investment and shortage investment indicates that a risk-seeker would like to have excess investment for securities whose return rates are bigger than the guaranteed return rates and shortage investment for securities whose return rates are smaller than the guaranteed return rates. Finally, we present three experiments to illustrate the proposed model. The results show that the different risk preferences derive different fuzzy portfolio selections under s and t dimensions, where a lower value of s is suggested for a risk-seeker as t > s, and we suggest the values of s and t to be smaller than or equal to 3. By contrast, for the risk-neutral investor, we suggest s = t; t < s is suggested to the investor who is risk-averse.

An Elliptic Intuitionistic Fuzzy Portfolio Selection Problem based on Knapsack Problem

“…According to [21], where the mean-variance model was used for portfolio selection and the risk the behavior of an investor in a different dimension distance for shortage investment and the excess investment was still not taken into account, the adjustable security proportion for excess investment and shortage investment based on the selected guaranteed return rates for profitable returns is suggested. The dimension of excess investment has been taken into consideration as the fuzzy portfolio based on guaranteed return rates has been developed for investors with various risk preferences [10]. According to Gorzaczany [19], since decision-makers aren't always able to accurately explain an element's degree of membership, formal representations of fuzzy sets are usually insufficient.…”