On the existence of solutions to the quadratic mixed-integer mean–variance portfolio selection problem

Corazza, Marco; Favaretto, Daniela

doi:10.1016/j.ejor.2005.10.053

Cited by 53 publications

(27 citation statements)

References 9 publications

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“…Traditionally, security returns were assumed to be random variables. A variety of mean-variance models have been constantly developed (e.g., Abdelaziz et al 2007;Corazza and Favaretto 2007;Hirschberger et al 2007;Liu et al 2003). As an improvement of mean-variance models, mean-semivariance models have been proposed employing semivariance as the measure of risk (Chow and Denning 1994;Grootveld and Hallerbach 1999;Markowitz 1959).…”

Section: Introductionmentioning

confidence: 99%

Minimax mean-variance models for fuzzy portfolio selection

Huang

2010

Soft Comput

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This paper discusses fuzzy portfolio selection problem in the situation where each security return belongs to a certain class of fuzzy variables but the exact fuzzy variable cannot be given. Two credibility-based minimax mean-variance models are proposed. The crisp equivalents of the models to linear programming ones are given in three special cases. In addition, a general solution algorithm is also provided. To help understand the modeling idea and to illustrate the effectiveness of the proposed algorithm, one example is presented.

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Section: Introductionmentioning

confidence: 99%

Minimax mean-variance models for fuzzy portfolio selection

Huang

2010

Soft Comput

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“…Traditionally, security returns were assumed to be random variables, and probability theory was the main tool for handling uncertainty. A great deal of achievements have been made in portfolio theory based on probability theory, for example, recent works Abdelaziz et al (2007); Corazza and Favaretto (2007); Hirschberger et al (2007); Huang (2008); Lin and Liu (2008), etc. However, the security market is complex and randomness is not the only type of uncertainty in reality.…”

Section: Introductionmentioning

confidence: 99%

Mean-risk model for uncertain portfolio selection

Huang

2010

Fuzzy Optim Decis Making

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This paper discusses the uncertain portfolio selection problem when security returns cannot be well reflected by historical data. It is proposed that uncertain variable should be used to reflect the experts' subjective estimation of security returns. Regarding the security returns as uncertain variables, the paper introduces a risk curve and develops a mean-risk model. In addition, the crisp form of the model is provided. The presented numerical examples illustrate the application of the mean-risk model and show the disaster result of mistreating uncertain returns as random returns.

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“…The key principle of the mean-variance model is to take the expected return of a portfolio as the investment return and to take the variance of the expected return of a portfolio as the investment risk, and security returns are assumed to be random variables. Following Markowitz's work, a number of portfolio selection models have been proposed in stochastic environment such as chance-constrained programming model [2,3], mean-absolute deviation model [4,5], mean-lower-partial moments model [6], minimax models [7,8] and various mean-variance models [9,10].…”

Section: Introductionmentioning

confidence: 99%

Mean-variance models for portfolio selection with fuzzy random returns

Hao

Liu

2008

J. Appl. Math. Comput.

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This paper develops two novel types of mean-variance models for portfolio selection problems, in which the security returns are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. In the proposed models, we take the expected return of a portfolio as the investment return and the variance of the expected return of a portfolio as the investment risk. We assume that the security returns are triangular fuzzy random variables. To solve the proposed portfolio problems, this paper first presents the variance formulas for triangular fuzzy random variables. Then this paper applies the variance formulas to the proposed models so that the original portfolio problems can be reduced to nonlinear programming ones. Due to the reduced programming problems include standard normal distribution in the objective functions, we cannot employ the conventional solution methods to solve them. To overcome this difficulty, this paper employs genetic algorithm (GA) to solve them, and verify the obtained optimal solutions via KuhnTucker (K-T) conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed models and methods.

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On the existence of solutions to the quadratic mixed-integer mean–variance portfolio selection problem

Cited by 53 publications

References 9 publications

Minimax mean-variance models for fuzzy portfolio selection

Minimax mean-variance models for fuzzy portfolio selection

Mean-risk model for uncertain portfolio selection

Mean-variance models for portfolio selection with fuzzy random returns

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