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<p>Consider a financial system comprising multiple individual companies. These companies jointly face a sequence of claim vectors arriving according to a Poisson process. Suppose that these companies make both risk-free and risky investments, with overall returns modeled by a geometric Brownian motion. In this dynamic, multidimensional setting, we introduce several systemic risk measures and conduct an asymptotic analysis of them. For claims that are heavy-tailed and either asymptotically dependent or asymptotically independent, we derive precise asymptotic formulas for the systemic risk measures. Numerical studies are carried out to evaluate the accuracy of these estimates, with particular emphasis on the roles of marginal tails and tail dependence.</p>

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Estimates for systemic risk measures in the presence of heavy tails

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Lei Zou,
  • Jiangyan Peng,
  • Chenghao Xu

摘要

Consider a financial system comprising multiple individual companies. These companies jointly face a sequence of claim vectors arriving according to a Poisson process. Suppose that these companies make both risk-free and risky investments, with overall returns modeled by a geometric Brownian motion. In this dynamic, multidimensional setting, we introduce several systemic risk measures and conduct an asymptotic analysis of them. For claims that are heavy-tailed and either asymptotically dependent or asymptotically independent, we derive precise asymptotic formulas for the systemic risk measures. Numerical studies are carried out to evaluate the accuracy of these estimates, with particular emphasis on the roles of marginal tails and tail dependence.