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Tail similarity

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  • Asimit, Vali
  • Yuan, Zhongyi
  • Zhou, Feng

Abstract

Simple tail similarity measures are investigated in this paper so that the overarching tail similarity between two distributions is captured. We develop some theoretical results to support our novel measures, where the focus is on asymptotic approximations of our similarity measures for Fréchet-type tails. A simulation study is provided to validate the effectiveness of our proposed measures and demonstrate their great potential in capturing the intricate tail similarity. We conclude that our measure and the standard comparisons between the (first-order) extreme index estimates provide complementary information, and one should analyze them in tandem rather than in isolation. We also provide a simple rule of thumb, summarized as a sequential decision rule, for using the two sources of information to assess tail similarity.

Suggested Citation

  • Asimit, Vali & Yuan, Zhongyi & Zhou, Feng, 2025. "Tail similarity," Insurance: Mathematics and Economics, Elsevier, vol. 121(C), pages 26-44.
    • Handle: RePEc:eee:insuma:v:121:y:2025:i:c:p:26-44
    DOI: 10.1016/j.insmatheco.2024.12.004
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    References listed on IDEAS

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    1. Mao, Tiantian & Lv, Wenhua & Hu, Taizhong, 2012. "Second-order expansions of the risk concentration based on CTE," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 449-456.
    2. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    3. Hua, Lei & Joe, Harry, 2011. "Second order regular variation and conditional tail expectation of multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 537-546.
    4. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    5. Birghila, Corina & Pflug, Georg Ch., 2019. "Optimal XL-insurance under Wasserstein-type ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 30-43.
    6. Castillo, Joan del & Serra, Isabel, 2015. "Likelihood inference for generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 116-128.
    7. Tang, Qihe & Yang, Yunshen, 2023. "Worst-case moments under partial ambiguity," ASTIN Bulletin, Cambridge University Press, vol. 53(2), pages 443-465, May.
    8. Mao, Tiantian & Stupfler, Gilles & Yang, Fan, 2023. "Asymptotic properties of generalized shortfall risk measures for heavy-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 173-192.
    9. Lux, Thibaut & Papapantoleon, Antonis, 2019. "Model-free bounds on Value-at-Risk using extreme value information and statistical distances," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 73-83.
    10. Ji, Liuyan & Tan, Ken Seng & Yang, Fan, 2021. "Tail dependence and heavy tailedness in extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 282-293.
    11. Qin, Xiao & Zhou, Chen, 2021. "Systemic risk allocation using the asymptotic marginal expected shortfall," Journal of Banking & Finance, Elsevier, vol. 126(C).
    12. Hong, Yongmiao & Liu, Yanhui & Wang, Shouyang, 2009. "Granger causality in risk and detection of extreme risk spillover between financial markets," Journal of Econometrics, Elsevier, vol. 150(2), pages 271-287, June.
    13. Hua Chen & J. David Cummins & Krupa S. Viswanathan & Mary A. Weiss, 2014. "Systemic Risk and the Interconnectedness Between Banks and Insurers: An Econometric Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(3), pages 623-652, September.
    14. Sun, Hongfang & Chen, Yu & Hu, Taizhong, 2022. "Statistical inference for tail-based cumulative residual entropy," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 66-95.
    15. Jose Blanchet & Henry Lam & Qihe Tang & Zhongyi Yuan, 2019. "Robust Actuarial Risk Analysis," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(1), pages 33-63, January.
    16. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
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