A portfolio selection model using fuzzy returns

Li, Duan; Stahlecker, Peter

doi:10.1007/s10700-011-9101-x

Cited by 19 publications

(6 citation statements)

References 15 publications

(11 reference statements)

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“…When we compare the dependencies (15)(16)(17)(18)(19) and (21)(22)(23)(24)(25), then we notice that for the case of decreasing unary operator G : R ⊃ A → R , its extension to OFNs differs from its extension to FNs. This is an important difference between OFNs and FNs.…”

Section: Definition 2 [124] For Any Upper Semi-continuous Non-decreasing Functionmentioning

confidence: 99%

“…FNs are also used in quantitative finance for modelling imprecision of financial data. In most of the papers regarding imprecision in finance, it is assumed a priori that the return rate from a security is a FN [19][20][21][22][23][24][25][26][27][28][29]. Yet, this assumption is connected, in most cases, to uncertain or unclear or incomplete information available to the investor.…”

Section: Introductionmentioning

confidence: 99%

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On Present Value Evaluation under the Impact of Behavioural Factors Using Oriented Fuzzy Numbers

Piasecki

Łyczkowska-Hanćkowiak

2021

Symmetry

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In general, the present value (PV) concept is ambiguous. Therefore, behavioural factors may influence on the PV evaluation. The main aim of our paper is to propose some method of soft computing PV evaluated under the impact of behavioural factors. The starting point for our discussion is the notion of the Behavioural PV (BPV) defined as an imprecisely real-valued function of distinguished variables which can be evaluated using objective financial knowledge or subjective behavioural premises. In our paper, a BPV is supplemented with a forecast of the asset price closest to changes. Such BPV is called the oriented BPV (O-BPV). We propose to evaluate an O-BPV by oriented fuzzy numbers which are more useful for portfolio analysis than fuzzy numbers. This fact determines the significance of the research described in this article. O-BPV may be applied as input signal for systems supporting invest-making. We consider here six cases of O-BPV: overvalued asset with the prediction of a rise in its price, overvalued asset with the prediction of a fall in its price, undervalued asset with the prediction of a rise in its price, undervalued asset with the prediction of a fall in its price, fully valued asset with the prediction of a rise in its rice and fully valued asset with the prediction of a fall in its rice. All our considerations are illustrated by numerical examples. Presented examples show the way in which we transform superposition of objective market knowledge and subjective investment opinion into simple return rate.

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Section: Definition 2 [124] For Any Upper Semi-continuous Non-decreasing Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Present Value Evaluation under the Impact of Behavioural Factors Using Oriented Fuzzy Numbers

Piasecki

Łyczkowska-Hanćkowiak

2021

Symmetry

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“…It allows for some of the parameters, considered in existing portfolio theory, such as return rate or present value [36][37][38] or probability distribution parameters [39], to be fuzzy. Fuzzy systems are increasingly used in portfolio analysis [40][41][42][43][44][45]. A detailed evolution of research was presented in [17,32].…”

Section: Introductionmentioning

confidence: 99%

The Use of Trapezoidal Oriented Fuzzy Numbers in Portfolio Analysis

Łyczkowska-Hanćkowiak

2021

Symmetry

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Oriented fuzzy numbers are a convenient tool to manage an investment portfolio as they enable the inclusion of uncertain and imprecise information about the financial market in a portfolio analysis. This kind of portfolio analysis is based on the discount factor. Thanks to this fact, this analysis is simpler than a portfolio analysis based on the return rate. The present value is imprecise due to the fact that it is modelled with the use of oriented fuzzy numbers. In such a case, the expected discount factor is also an oriented fuzzy number. The main objective of this paper is to conduct a portfolio analysis consisting of the instruments with the present value estimated as a trapezoidal oriented fuzzy number. We consider the portfolio elements as being positively and negatively oriented. We test their discount factor. Due to the fact that adding oriented fuzzy numbers is not associative, a weighted sum of positively oriented discount factors and a weighted sum of negatively oriented factors is calculated and consequently a portfolio discount factor is obtained as a weighted addition of both sums. Also, the imprecision risk of the obtained investment portfolio is estimated using measures of energy and entropy. All theoretical considerations are illustrated by an empirical case study.

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“…Therefore, it is almost impossible to determine random distributions of future returns. As a nonprobabilistic approach, many researchers proposed fuzzy-based portfolio selection problems using the fuzzy theory (Bilbao-Terol et al [7], Carlsson et al [8], Duan and Stahlecker [9], Huang [10,11], Inuiguchi and Tanino [12], Tanaka et al [13,14], and Watada [15]). Furthermore, some researchers proposed portfolio models with both randomness and fuzziness, for instance, fuzzy random portfolio selection problems (Katagiri et al [16]) and random fuzzy portfolio selection problems (Hasuike et al [17], Huang [18]).…”

Section: Introductionmentioning

confidence: 99%

Risk-Controlled Multiobjective Portfolio Selection Problem Using a Principle of Compromise

Hasuike

Katagiri

2014

Mathematical Problems in Engineering

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This paper proposes a multiobjective portfolio selection problem with most probable random distribution derived from current market data and other random distributions of boom and recession under the risk-controlled parameters determined by an investor. The current market data and information include not only historical data but also interpretations of economists’ oral and linguistic information, and hence, the boom and recession are often caused by these nonnumeric data. Therefore, investors need to consider several situations from most probable condition to boom and recession and to avoid the risk less than the target return in each situation. Furthermore, it is generally difficult to set random distributions of these cases exactly. Therefore, a robust-based approach for portfolio selection problems using the only mean values and variances of securities is proposed as a multiobjective programming problem. In addition, an exact algorithm is developed to obtain an explicit optimal portfolio using a principle of compromise.

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A portfolio selection model using fuzzy returns

Cited by 19 publications

References 15 publications

On Present Value Evaluation under the Impact of Behavioural Factors Using Oriented Fuzzy Numbers

On Present Value Evaluation under the Impact of Behavioural Factors Using Oriented Fuzzy Numbers

The Use of Trapezoidal Oriented Fuzzy Numbers in Portfolio Analysis

Risk-Controlled Multiobjective Portfolio Selection Problem Using a Principle of Compromise

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