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

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