A polynomial goal programming model for portfolio optimization based on entropy and higher moments

Aksaraylı, Mehmet; Pala, Osman

doi:10.1016/j.eswa.2017.10.056

Cited by 61 publications

(27 citation statements)

References 30 publications

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“…Considering the complexity of the market environment, we measure risk from different aspects to construct portfolio selection models to help investors with different risk preferences. In order to deal with the multi-objective problem, we introduce the PGP method mentioned in [31], transforming multiple targets into a single target, and further effectively compare the different risk indicators. Specifically, we apply the defuzzification approach introduced in Section 2 to obtain crisp forms of objective functions.…”

Section: The Multi-period Polynomial Goal Programming Modelmentioning

confidence: 99%

“…Similar to Lai [32], first normalize the Minkowski distance, and then, we can get a standardized expression. Furthermore, with reference to Aksarayli and Pala [31], we added one to all normalized goals, guaranteeing the base number of each objective to be greater than one, so that the goal variables can increase strictly with the exponent. Then, considering the investors' preferences for the model, λ i was utilized to prioritize the five targets.…”

Section: The Multi-period Polynomial Goal Programming Modelmentioning

confidence: 99%

“…Besides, similar to Aksarayli and Pala [31] and DeMiguel and Nogales [33], we compared portfolio models with average portfolio turnover (PT) as a value of the magnitude of the transaction cost in different periods, which is computed as:…”

Section: Portfolio Performance Measuresmentioning

confidence: 99%

See 2 more Smart Citations

Performance of Different Risk Indicators in a Multi-Period Polynomial Portfolio Selection Problem Based on the Credibility Measure

Zhou

Shen

Zhao

et al. 2019

Entropy

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In this paper, we study the portfolio selection problem considering transaction costs under multiple periods. For non-professional investors, it is a critical factor to choose an appropriate model among multiple portfolio selection models in investment. Based on the credibility measure, we formulate a multi-period polynomial portfolio selection model to gather the risk indicators involving variance, semi-variance, entropy, and semi-entropy, helping investors bet on assets. According to the polynomial goal programming (PGP) approach, investors can conquer the fields by combining apposite indicators to build appropriate models. Subsequently, an adjusted genetic algorithm on the foundation of the penalty function is designed to obtain the optimal solution of this multi-period model. The results indicate that the PGP method is suitable for investors to choose the model and assigns the proper models to investors with different risk preferences.

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Section: The Multi-period Polynomial Goal Programming Modelmentioning

confidence: 99%

Section: The Multi-period Polynomial Goal Programming Modelmentioning

confidence: 99%

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Performance of Different Risk Indicators in a Multi-Period Polynomial Portfolio Selection Problem Based on the Credibility Measure

Zhou

Shen

Zhao

et al. 2019

Entropy

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“…In [1], the authors presented the different variants of the goal programming model that has been applied to the financial portfolio selection problem. In [2], the authors optimized the portfolio based on entropy and higher moments by using a polynomial goal programming model, and the results indicated that the proposed method is suited for portfolio models which have higher moments. Portfolio optimization techniques also significantly improved the return-risk tradeoff performances using multiobjective evolutionary model proposed in [3].…”

Section: Introductionmentioning

confidence: 99%

Applying Least Squares Support Vector Machines to Mean‐Variance Portfolio Analysis

Wang

Kim

2019

Mathematical Problems in Engineering

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Portfolio selection problem introduced by Markowitz has been one of the most important research fields in modern finance. In this paper, we propose a model (least squares support vector machines (LSSVM)-mean-variance) for the portfolio management based on LSSVM. To verify the reliability of LSSVM-mean-variance model, we conduct an empirical research and design an algorithm to illustrate the performance of the model by using the historical data from Shanghai stock exchange. The numerical results show that the proposed model is useful when compared with the traditional Markowitz model. Comparing the efficient frontier and total wealth of both models, our model can provide a more measurable standard of judgment when investors do their investment.

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“…Amritansu Ray and Sanat Kumar Majumder[6] proposed a new non-Shannon fuzzy mean-variance-skewness-entropy model, which established a multi-objective non-linear portfolio model by maximizing mean and skewness and minimizing variance and cross-entropy. Mehmet Aksarayli and Osman Pala[7] proposed a…”

mentioning

confidence: 99%

High Order Portfolio Optimization Problem with Transaction Costs

Li¹,

Zhang²

2019

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This paper studies a high order moments portfolio optimization model with transaction costs. The model takes kurtosis as objective function and takes the skewness, variance, mean and transaction costs as constraints conditions. Since the optimization problem is of high order and non-convex, it brings some difficulties to the solution of the model. Therefore, this paper transforms the optimization problem into a semi-definite matrix optimization problem by using the moment matrix theory, and then solves it. Through the study of four risky assets in China's securities market, it is found that transaction costs are significant parts in the study of portfolio model. In addition, sensitivity analysis shows that the kurtosis and skewness are positively correlated with the mean and variance invariant. When mean and skewness are constant, kurtosis and variance are positively correlated. When mean and skewness remain unchanged, the fourth order standard central moment and variance are negatively correlated.

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A polynomial goal programming model for portfolio optimization based on entropy and higher moments

Cited by 61 publications

References 30 publications

Performance of Different Risk Indicators in a Multi-Period Polynomial Portfolio Selection Problem Based on the Credibility Measure

Performance of Different Risk Indicators in a Multi-Period Polynomial Portfolio Selection Problem Based on the Credibility Measure

Applying Least Squares Support Vector Machines to Mean‐Variance Portfolio Analysis

High Order Portfolio Optimization Problem with Transaction Costs

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