Abstract

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.

Information

Preprint No.SS-2024-0418
Manuscript IDSS-2024-0418
Complete AuthorsQingzhao Zhong, Yanxi Hou
Corresponding AuthorsYanxi Hou
Emailsyxhou@fudan.edu.cn

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Acknowledgments

Yanxi Hou’s work was supported by the National Natural Science Foundation of China under Grant Nos. 72171055 and 71991471.

Supplementary Materials

The online Supplementary Material contains some theoretical statements,

auxiliary results, all technical proofs and additional simulation results.

Supplementary materials are available for download.