On the Shortfall of Tail-Based Entropy and Its Application to Capital Allocation.

ABSTRACT: We introduce and study the shortfall of tail-based entropy (STE), a tail-sensitive risk functional that combines expected shortfall (ES) and tail-based entropy (TE). Beyond the tail mean, STE imposes a rank-dependent penalty on tail variability, thereby capturing both the magnitude and variability of tail risk under extremes. The framework encompasses several shortfall-type measures as special cases, such as Gini shortfall, extended Gini shortfall, shortfall of cumulative residual entropy, shortfall of right-tail deviation, and shortfall of cumulative residual Tsallis entropy. We provide equivalent characterizations of STE, derive sufficient conditions for coherence, and establish monotonicity with respect to tail-variability order. As an application, we investigate STE-based capital alloc

SUBMITTER: Li P 

PROVIDER: S-EPMC12651032 | biostudies-literature | 2025 Nov

REPOSITORIES: biostudies-literature