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Partial Gini Coefficient for Uncertain Random Variables with Application to Portfolio Selection

Author

Listed:
  • Lifeng Wang

    (School of Business, Qingdao University, Qingdao 266071, China)

  • Jinwu Gao

    (School of Economics, Ocean University of China, Qingdao 266100, China)

  • Hamed Ahmadzade

    (Department of Statistics, University of Sistan and Baluchestan, Zahedan 98155-987, Iran)

  • Zezhou Zou

    (School of Economics, Ocean University of China, Qingdao 266100, China)

Abstract

The partial Gini coefficient measures the strength of dispersion for uncertain random variables, while controlling for the effects of all random variables. Similarly to variance, the partial Gini coefficient plays an important role in uncertain random portfolio selection problems, as a risk measure to find the optimal proportions for securities. We first define the partial Gini coefficient as a risk measure in uncertain random environments. Then, we obtain a computational formula for computing the partial Gini coefficient of uncertain random variables. Moreover, we apply the partial Gini coefficient to characterize risk of investment and investigate a mean-partial Gini model with uncertain random returns. To display the performance of the mean-partial Gini portfolio selection model, some computational examples are provided. To compare the mean-partial Gini model with the traditional mean-variance model using performance ratio and diversification indices, we apply Wilcoxon non-parametric tests for related samples.

Suggested Citation

  • Lifeng Wang & Jinwu Gao & Hamed Ahmadzade & Zezhou Zou, 2023. "Partial Gini Coefficient for Uncertain Random Variables with Application to Portfolio Selection," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3929-:d:1240813
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    References listed on IDEAS

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    3. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
    4. Qin, Zhongfeng, 2015. "Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 480-488.
    5. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
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