Possibilistic mean–variance models and efficient frontiers for portfolio selection problem

Zhang, Weiguo; Ying-luo, Wang; Chen, Zhiping; Nie, Zaiping

doi:10.1016/j.ins.2007.01.030

Cited by 128 publications

(42 citation statements)

References 35 publications

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“…Ammar (2008) solved the fuzzy portfolio optimization problem as a convex quadratic programming. Zhang et al (2007) presented two types of portfolio selection models based on lower and upper possibilistic means and variances, respectively, and introduced the notions of lower and upper possibilistic efficient portfolio. Li et al (2010) stated that portfolio returns are generally asymmetric, and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are the same.…”

Section: Literature Reviewmentioning

confidence: 99%

A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

Gharakhani¹,

Sadjadi²

2013

dsl

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In this paper, we examine advanced optimization approach for portfolio problem introduced by Black and Litterman to consider the shortcomings of Markowitz standard Mean-Variance optimization. Black and Litterman propose a new approach to estimate asset return. They present a way to incorporate the investor's views into asset pricing process. Since the investor's view about future asset return is always subjective and imprecise, we can represent it by using fuzzy numbers and the resulting model is multi-objective linear programming. Therefore, the proposed model is analyzed through fuzzy compromise programming approach using appropriate membership function. For this purpose, we introduce the fuzzy ideal solution concept based on investor preference and indifference relationships using canonical representation of proposed fuzzy numbers by means of their correspondingα-cuts. A real world numerical example is presented in which MSCI (Morgan Stanley Capital International Index) is chosen as the target index. The results are reported for a portfolio consisting of the six national indices. The performance of the proposed models is compared using several financial criteria.

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Section: Literature Reviewmentioning

confidence: 99%

A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

Gharakhani¹,

Sadjadi²

2013

dsl

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“…Considering the complexity of the security market in the real world, the non-uniqueness of randomness as a kind of uncertainty and the lack of enough historical data to reflect the future performances of security returns in some real life cases, many scholars began to regard security returns as fuzzy variables which rely on experienced experts' evaluations instead of historical data. Thus, fuzzy portfolio optimization theory is developed and has been mainly studied based on following three methods: (i) Fuzzy set theory [5]; (ii) Possibility measure [6,7]; (iii) Credibility measure [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

Gao

Huicheng

2017

Entropy

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This paper aims to develop a risk-free protection index model for portfolio selection based on the uncertain theory. First, the returns of risk assets are assumed as uncertain variables and subject to reputable experts' evaluations. Second, under this assumption, combining with the risk-free interest rate we define a risk-free protection index (RFPI), which can measure the protection degree when the loss of risk assets happens. Third, note that the proportion entropy serves as a complementary means to reduce the risk by the preset diversification requirement. We put forward a risk-free protection index model with an entropy constraint under an uncertainty framework by applying the RFPI, Huang's risk index model (RIM), and mean-variance-entropy model (MVEM). Furthermore, to solve our portfolio model, an algorithm is given to estimate the uncertain expected return and standard deviation of different risk assets by applying the Delphi method. Finally, an example is provided to show that the risk-free protection index model performs better than the traditional MVEM and RIM.

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“…In this situation, a better way is to estimate security returns by experienced experts such as fund managers, which implies that security returns are fuzzy variables. Several researchers (Wang and Zhu, 2002;Terol et al, 2006;Fang et al, 2006;Vercher et al, 2007;, Zhang et al, 2007, Zhang et al, , 2009Huang, 2008;Li et al, 2010;Liu and Liu, 2002;Huang, 2008;Li et al, 2010; have utilized fuzzy set theory to investigate portfolio selection problem by regarding security returns as fuzzy variables instead of random variables. Different from random variables and fuzzy variables, Liu (2007) proposed the concept of uncertain variable and established uncertainty theory to study the behavior of uncertain phenomena.…”

Section: Introductionmentioning

confidence: 99%

Multiperiod Mean Absolute Deviation Uncertain Portfolio Selection

Zhang¹

2016

Industrial Engineering and Management Systems

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Multiperiod portfolio selection problem attracts more and more attentions because it is in accordance with the practical investment decision-making problem. However, the existing literature on this field is almost undertaken by regarding security returns as random variables in the framework of probability theory. Different from these works, we assume that security returns are uncertain variables which may be given by the experts, and take absolute deviation as a risk measure in the framework of uncertainty theory. In this paper, a new multiperiod mean absolute deviation uncertain portfolio selection models is presented by taking transaction costs, borrowing constraints and threshold constraints into account, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on uncertain theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. To solve the new model in general cases, the forward dynamic programming method is presented. In addition, a numerical example is also presented to illustrate the modeling idea and the effectiveness of the designed algorithm.

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Possibilistic mean–variance models and efficient frontiers for portfolio selection problem

Cited by 128 publications

References 35 publications

A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

Multiperiod Mean Absolute Deviation Uncertain Portfolio Selection

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