Extreme Behaviors in Risk Measurement via Joint Tail-Based Cumulative Residual Entropy and Its Generalized Version

Abstract

Tail risk analysis plays a pivotal strategic role in risk management, particularly in light of economic crises. In this context, the purpose of this paper is to examine the asymptotic properties of Joint Tail-based Cumulative Residual Entropy ( $JTCRE$ ) in a bivariate setup involving two variables, $X$ and $Y$ . In this setup, $X$ is considered the variable of interest, while $Y$ serves as the benchmark variable. We provide a generalization of the Joint Tail-based Cumulative Residual Entropy to create a more flexible version that allows for a more comprehensive analysis of extreme risk. This generalization leads to a deeper understanding of the tail relationship between $X$ and $Y$ and their respective impacts on a specific system. To illustrate our results, we conducted the study under both tail-dependent and tail-independent scenarios. We supplemented our research with practical examples and applied our findings to real-world financial data, employing our proposed non-parametric estimator of $JTCRE$ as the basis for our analysis.