TY - JOUR
T1 - Uncertainty Comparison Between Value-at-Risk and Expected Shortfall
AU - Liu , Qing
AU - Liu , Weimin
AU - Peng , Liang
AU - Qin , Gengsheng
JO - Communications in Mathematical Research 
VL - 1
SP - 102
EP - 124
PY - 2023
DA - 2023/12
SN - 40
DO - http://doi.org/10.4208/cmr.2022-0071
UR - https://global-sci.org/intro/article_detail/cmr/22283.html
KW - $α$-mixing, asymptotic variance, expected shortfall, Value-at-Risk.
AB - <p style="text-align: justify;">Value-at-Risk (VaR) and expected shortfall (ES) are two key risk measures in financial risk management. Comparing these two measures has been
a hot debate, and most discussions focus on risk measure properties. This paper uses independent data and autoregressive models with normal or $t$-distribution to examine the effect of the heavy tail and dependence on comparing
the nonparametric inference uncertainty of these two risk measures. Theoretical and numerical analyses suggest that VaR at 99% level is better than ES at
97.5% level for distributions with heavier tails.</p>