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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. 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.
    2. 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.
    3. 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.

    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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