Extreme risk modeling based on Tail Extended Gini and Joint Tail Extended Gini

The concept of tail variability in statistical analysis plays a central role in various fields, including economics, finance, and public policy. In this context, this paper aims to explore the asymptotic properties of Tail Extended Gini-type measures for a bivariate random vector ( X , Y ) {(X,Y)} , where X represents the examined loss variable and Y serves as a benchmark variable. Within this framework, we introduce a new measure of variability called the Joint Tail Extended Gini, which considers the tail characteristics of both X and Y. Specifically, we examine the asymptotic properties of the proposed measure, taking into consideration the degree of risk aversion of investors. Additionally, we generalize the Joint Tail-Gini functional in order to provide a more flexible risk measure. Subsequently, we present examples and demonstrate a practical application of our results. These findings have significant implications for understanding the extreme behaviors of investors and can be applied in various fields, including decision-making, to measure and analyze tail risk.