Tail Risk Equivalent Level Transition And Its Application for Estimating Extreme Lp-Quantiles

Lp-quantiles, as a generalization of Value-at-Risk and expectile, have gained increasing attention in risk management due to their feasibility and straightforwardness in statistical implementation.This paper introduces the concept of Tail Risk Equivalent Level Transition (TRELT) to capture changes in tail risk when transitioning between two Lp-quantiles.Motivated by PELVE in Li and Wang (2023) but tailored for tail risk, we investigate the theoretical properties of TRELT, including its existence, uniqueness, and asymptotic behavior.Additionally, we develop inference methods for TRELT and extreme Lp-quantiles using this risk transition, which serves as a novel extrapolation technique in extreme value theory.Simulation studies and real data analysis demonstrate the empirical performance of these methods.