An asymptotic study of systemic expected shortfall and marginal expected shortfall

Yiqing Chen, Jiajun Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)238-251
Number of pages14
JournalInsurance: Mathematics and Economics
Volume105
DOIs
Publication statusPublished - Jul 2022

Keywords

  • Asymptotic independence
  • Heavy-tailed distributions
  • Random weights
  • Regular variation
  • Systemic risk

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