Abstract

Tail Gini functional is a measure of tail risk variability for systemic

risks, and has many applications in banking, finance and insurance. Meanwhile,

there is growing attention on asymptotic independent pairs in quantitative risk

management. This paper addresses the estimation of the tail Gini functional

under asymptotic independence. We first estimate the tail Gini functional at an

intermediate level and then extrapolate it to the extreme tails. The asymptotic

normalities of both the intermediate and extreme estimators are established. The

simulation study shows that our estimator performs comparatively well in view

of both bias and variance.

The application to measure the tail variability of

weekly loss of individual stocks given the occurrence of extreme events in the

market index in Hong Kong Stock Exchange provides meaningful results, and

leads to new insights in risk management.

Information

Preprint No.SS-2023-0426
Manuscript IDSS-2023-0426
Complete AuthorsZhaowen Wang, Liujun Chen, Deyuan Li
Corresponding AuthorsDeyuan Li
Emailsdeyuanli@fudan.edu.cn

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Acknowledgments

The authors thank the editor, associate editor, and reviewers for their

valuable comments and suggestions.

Deyuan Li’s research was partially

supported by the National Natural Science Foundation of China grants

11971115 and 12471279. Liujun Chen’s research was partially supported

by the National Natural Science Foundation of China grants 12301387 and

12471279.

Supplementary Materials

The supplementary material contains the proofs of four auxiliary lemmas

and Proposition 1 as well as some additional figures for the Simulation and

Application.

Supplementary materials are available for download.