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The conditional higher moment risk measure: second-order asymptotics with FGM contagion

Author

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  • Haifan Hu
  • Bingzhen Geng
  • Jiajun Liu
  • Shijie Wang

Abstract

This paper investigates second-order asymptotic expansions for the conditional higher moment (CoHM) coherent risk measure under a Farlie-Gumbel-Morgenstern (FGM) dependence structure, capturing a weak contagion between a primary loss risk and a reference risk. Assuming that the primary risk belongs to the Fr\'echet, Weibull, or Gumbel maximum domain of attraction, we systematically derive second-order asymptotic expansions using extreme value theory and second-order regular variation theory. Compared with existing first-order results, our refined approximations capture higher-order tail behavior and dependence effects more accurately. Numerical simulations confirm that the second-order asymptotics substantially reduce approximation errors, especially at extreme confidence levels. Empirical applications to insurance claim data further illustrate the practical superiority of the second-order approach.

Suggested Citation

  • Haifan Hu & Bingzhen Geng & Jiajun Liu & Shijie Wang, 2026. "The conditional higher moment risk measure: second-order asymptotics with FGM contagion," Papers 2607.16601, arXiv.org.
    • Handle: RePEc:arx:papers:2607.16601
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    File URL: https://arxiv.org/pdf/2607.16601
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