TY - JOUR
T1 - An asymptotic study of systemic expected shortfall and marginal expected shortfall
AU - Chen, Yiqing
AU - Liu, Jiajun
N1 - Funding Information:
The authors would like to thank the two anonymous referees and the editor for their careful reading and valuable comments, which have helped significantly improve the quality of the manuscript. The research of Yiqing Chen was supported by a Centers of Actuarial Excellence (CAE) Research Grant ( 2018–2022 ) from the Society of Actuaries (SOA), USA, and a Summer Research Grant (2021) from the College of Business and Public Administration at Drake University , USA. The research of Jiajun Liu was supported by the National Natural Science Foundation of China (NSFC: 72171055 ), the Natural Science Foundation of Jiangsu Higher Education Institutions (No. 21KJB110019 ), the XJTLU Postgraduate Research Scholarship ( PGRS2012012 , FOSA200701 , FOSA200702 ), and the XJTLU University Research Fund Project ( RDF-17-01-21 ).
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/7
Y1 - 2022/7
N2 - 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.
AB - 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.
KW - Asymptotic independence
KW - Heavy-tailed distributions
KW - Random weights
KW - Regular variation
KW - Systemic risk
UR - http://www.scopus.com/inward/record.url?scp=85129464226&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2022.04.009
DO - 10.1016/j.insmatheco.2022.04.009
M3 - Article
SN - 0167-6687
VL - 105
SP - 238
EP - 251
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -