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An asymptotic study of systemic expected shortfall and marginal expected shortfall

Author

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  • Chen, Yiqing
  • Liu, Jiajun

Abstract

Following recent studies of systemic risk in banking, finance, and insurance, we quantify systemic expected shortfall (SES) and marginal expected shortfall (MES) in a general context of quantitative risk management and link them to a confidence level q∈(0,1). For this purpose, we consider a system comprising multiple individuals (sub-portfolios, lines of business, or entities) whose loss-profit variables are modeled by randomly weighted random variables so that both their tail behavior and the interdependence among them are captured. For the case of heavy-tailed losses, we derive general asymptotic formulas for the SES and MES as q↑1. If restricted to the special case in which the losses have equivalent regularly varying tails, the obtained formulas are further simplified and explicitized into the value at risk of a representing random variable. Numerical studies are conducted to examine the performance of these asymptotic formulas.

Suggested Citation

  • Chen, Yiqing & Liu, Jiajun, 2022. "An asymptotic study of systemic expected shortfall and marginal expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 238-251.
    • Handle: RePEc:eee:insuma:v:105:y:2022:i:c:p:238-251
    DOI: 10.1016/j.insmatheco.2022.04.009
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    Citations

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    Cited by:

    1. Wang, Bingjie & Li, Jinzhu, 2024. "Asymptotic results on tail moment for light-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 43-55.
    2. Bingzhen Geng & Yang Liu & Hongfu Wan, 2024. "Systemic Risk Asymptotics in a Renewal Model with Multiple Business Lines and Heterogeneous Claims," Papers 2410.00158, arXiv.org.
    3. Zhangting Chen & Dongya Cheng, 2024. "On the Tail Behavior for Randomly Weighted Sums of Dependent Random Variables with its Applications to Risk Measures," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-27, December.
    4. Bingzhen Geng & Yang Liu & Yimiao Zhao, 2024. "Value-at-Risk- and Expectile-based Systemic Risk Measures and Second-order Asymptotics: With Applications to Diversification," Papers 2404.18029, arXiv.org.
    5. Radu LUPU & Iulia LUPU & Tanase STAMULE & Mihai ROMAN, 2022. "Entropy as Leading Indicator for Extreme Systemic Risk Events," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 58-73, December.

    More about this item

    Keywords

    Systemic risk; Heavy-tailed distributions; Random weights; Asymptotic independence; Regular variation;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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