Abstract
This research sets the basis for modeling the performance indicators of financial assets using triangular neutrosophic fuzzy numbers. This type of number allows for the modeling of financial assets performance indicators by taking into consideration all the possible scenarios of their achievement. The key performance indicators (KPIs) modeled with the help of triangular fuzzy neutrosophic numbers are the return on financial assets, the financial assets risk, and the covariance between financial assets. Thus far, the return on financial assets has been studied using statistical indicators, like the arithmetic and geometric mean, or using the financial risk indicators with the help of the squared deviations from the mean and covariance. These indicators are well known as the basis of portfolio theory. This paper opens the perspective of modeling these three mentioned statistical indicators using triangular neutrosophic fuzzy numbers due to the major advantages they have. The first advantage of the neutrosophic approach is that it includes three possible symmetric scenarios of the KPIs achievement, namely the scenario of certainty, the scenario of non-realization, and the scenario of indecision, in which it cannot be appreciated whether the performance indicators are or are not achieved. The second big advantage is its data series clustering, representing the financial performance indicators by which these scenarios can be delimitated by means of neutrosophic fuzzy numbers in very good, good or weak performance indicators. This clustering is realized by means of the linguistic criteria and measuring the belonging degree to a class of indicators using fuzzy membership functions. The third major advantage is the selection of risk mitigation analysis scenarios and the formation of financial assets’ optimal portfolios.
Highlights
Financial markets specialists have shown a particular interest for financial assets lately, both due to returns they generate for investors and because they can predict the future evolution of financial performance [1]
The aim of this paper is to properly model the indicators from portfolio theory using triangular neutrosophic fuzzy numbers while solving the problems that arise in the classical approach—these being several limitations which might appear in the case of the financial assets’ performance indicators use
Modeling these three performance indicators of the financial assets has been achieved with the help of triangular neutrosophic fuzzy numbers, which presents a number of advantages:
Summary
Financial markets specialists have shown a particular interest for financial assets lately, both due to returns they generate for investors and because they can predict the future evolution of financial performance [1]. The risk assumed by investors can be manifested with different intensities (this risk may take maximum or minimum values, and there is an area where the risk intensity is uncertain) This degree of uncertainty for the obtaining of the financial asset return, noted as (Du (Ra )), can be grouped into three main categories:. The third category: The degree for obtaining the financial asset return is uncertain, denoted by λ(Du (σa, Ra )), corresponding to the situation in which the realization or non-realization of the return is uncertain or not appreciated This area of uncertainty is approximated at 20%, and it is specific to each category of financial assets. The introduction of these criteria for assessing financial asset return allows for the analysis of these performance indicators in line with the real needs of investors. The aim of this paper is to properly model the indicators from portfolio theory using triangular neutrosophic fuzzy numbers (considering the major advantages they provide) while solving the problems that arise in the classical approach—these being several limitations which might appear in the case of the financial assets’ performance indicators use
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