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This paper aims to model the covariance of financial assets using neutrosophic fuzzy numbers. Two main concepts are discussed and used, namely the neutrosophic covariance of the financial assets and the independent neutrosophic portfolios. In terms of methodology, a three-step approach is proposed with the purpose of identifying the independent neutrosophic portfolio return, the independent neutrosophic portfolio risk and the structure of the independent neutrosophic portfolio. For this purpose, neutrosophic fuzzy theory is chosen for this type of approach as it allows a proper modeling of the financial performance indicators by taking into account the probabilities of their achievement. This action is possible even in the situation in which linguistic variables are used for better characterizing the values of the recorded data. Numerical examples are provided in each stage of the methodology description for a better understanding of the proposed approach. The results of the study can be used to substantiate the decisions made by the capital market investors. Full article

The purpose of this paper was to model, with the help of neutrosophic fuzzy numbers, the optimal financial asset portfolios, offering additional information to those investing in the capital market. The optimal neutrosophic portfolios are those categories of portfolios consisting of two or more financial assets, modeled using neutrosophic triangular numbers, that allow for the determination of financial performance indicators, respectively the neutrosophic average, the neutrosophic risk, for each financial asset, and the neutrosophic covariance as well as the determination of the portfolio return, respectively of the portfolio risk. There are two essential conditions established by rational investors on the capital market to obtain an optimal financial assets portfolio, respectively by fixing the financial return at the estimated level as well as minimizing the risk of the financial assets neutrosophic portfolio. These conditions allowed us to compute the financial assets’ share in the total value of the neutrosophic portfolios, for which the financial return reaches the level set by investors and the financial risk has the minimum value. In financial terms, the financial assets’ share answers the legitimate question of rational investors in the capital market regarding the amount of money they must invest in compliance with the optimal conditions regarding the neutrosophic return and risk. Full article

This paper studies the problem of neutrosophic portfolios of financial assets as part of the modern portfolio theory. Neutrosophic portfolios comprise those categories of portfolios made up of financial assets for which the neutrosophic return, risk and covariance can be determined and which provide concomitant information regarding the probability of achieving the neutrosophic return, both at each financial asset and portfolio level and also information on the probability of manifestation of the neutrosophic risk. Neutrosophic portfolios are characterized by two fundamental performance indicators, namely: the neutrosophic portfolio return and the neutrosophic portfolio risk. Neutrosophic portfolio return is dependent on the weight of the financial assets in the total value of the portfolio but also on the specific neutrosophic return of each financial asset category that enters into the portfolio structure. The neutrosophic portfolio risk is dependent on the weight of the financial assets that enter the portfolio structure but also on the individual risk of each financial asset. Within this scientific paper was studied the minimum neutrosophic risk at the portfolio level, respectively, to establish what should be the weight that the financial assets must hold in the total value of the portfolio so that the risk is minimum. These financial assets weights, after calculations, were found to be dependent on the individual risk of each financial asset but also on the covariance between two financial assets that enter into the portfolio structure. The problem of the minimum risk that characterizes the neutrosophic portfolios is of interest for the financial market investors. Thus, the neutrosophic portfolios provide complete information about the probabilities of achieving the neutrosophic portfolio return but also of risk manifestation probability. In this context, the innovative character of the paper is determined by the use of the neutrosophic triangular fuzzy numbers and by the specific concepts of financial assets, in order to substantiating the decisions on the financial markets. Full article

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. Full article