Estimation Of The Quantile Shortfall Based On VaR And ES

Extreme risk exists in financial investment,credit,insurance and other fields.It directly affects the economic life,and also affects a country's macro decision-making and economic development.It has become one of the important tasks of institutions and enterprises to manage and prevent many kinds of risk.Among recent measures for risk management,Value at Risk(VaR)which measures the maximum potential loss of a given portfolio over a prescribed holding period at a given confidence level has been criticized for it is not coherent.Expected Shortfall(ES)as an alternative risk measure which is the mean of the tail loss distribution has also been criticized for it is susceptible to outliers and not robust.Median Shortfall(MS)as an alternative risk measure calcu-lates the median of the tail loss distribution.It has distributional robustness and is easy to implement.A new risk measure called Quantile Shortfall(QS)which measures the conditional quantile loss of the tail risk is motivated in this paper.We first construct an estimator of the QS and establish the asymptotic normality behaviour of the estimator.The finite sample performance of the estimator and relevance of the limit theorem are evaluated through simulation studies.The results show that the large sample properties of the proposed estimator perform well,which implies the risk measure QS has good properties in financial institutions.