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<p>Risk measures for systemic risk become more and more important in recent years, and various systemic risk measures have been provided in the literature. We consider a static model of <i>n</i> individuals generated by terminal losses <i>X</i><sub><i>i</i></sub> and stochastic discount factors <i>θ</i><sub><i>i</i></sub> (<i>i</i> = 1, 2,…, <i>n</i>) in a general context. We quantify systemic expected shortfall (SES) and marginal expected shortfall (MES), which are linked to a confidence level <i>q</i> ∈ (0<i>,</i> 1) in this static model. Under the condition that there exists a dependence structure between the terminal losses <i>X</i><sub><i>i</i></sub>, 1 ≤ <i>i</i> ≤ <i>n</i>, in heavy-tailed phenomena, the asymptotic results for (SES) and MES are obtained as <i>q</i> → 1. Numerical studies are carried out to check the performance of the asymptotic results.</p>

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Asymptotic estimates for systemic risk with dependent heavy-tailed losses

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • Chenghao Xu,
  • Jiangyan Peng,
  • Lei Zou

摘要

Risk measures for systemic risk become more and more important in recent years, and various systemic risk measures have been provided in the literature. We consider a static model of n individuals generated by terminal losses Xi and stochastic discount factors θi (i = 1, 2,…, n) in a general context. We quantify systemic expected shortfall (SES) and marginal expected shortfall (MES), which are linked to a confidence level q ∈ (0, 1) in this static model. Under the condition that there exists a dependence structure between the terminal losses Xi, 1 ≤ i ≤ n, in heavy-tailed phenomena, the asymptotic results for (SES) and MES are obtained as q → 1. Numerical studies are carried out to check the performance of the asymptotic results.