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

Lifeng Wang, Jinwu Gao (), Hamed Ahmadzade and Zezhou Zou ()
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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

Mathematics, 2023, vol. 11, issue 18, 1-18

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.

Keywords: performance ratio; diversification index; uncertain random variables; inverse uncertainty distribution; portfolio selection; Gini coefficient (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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