Chun, So Yeon; Shapiro, Alexander; Uryasev, Stan Conditional value-at-risk and average value-at-risk: estimation and asymptotics. (English) Zbl 1260.91121 Oper. Res. 60, No. 4, 739-756 (2012). Summary: We discuss linear regression approaches to the estimation of law-invariant conditional risk measures. Two estimation procedures are considered and compared; one is based on residual analysis of the standard least-squares method, and the other is in the spirit of the M-estimation approach used in robust statistics. In particular, value-at-risk and average value-at-risk measures are discussed in detail. Large sample statistical inference of the estimators is derived. Furthermore, finite sample properties of the proposed estimators are investigated and compared with theoretical derivations in an extensive Monte Carlo study. Empirical results on the real data (different financial asset classes) are also provided to illustrate the performance of the estimators. Cited in 1 ReviewCited in 19 Documents MSC: 91B30 Risk theory, insurance (MSC2010) 62J05 Linear regression; mixed models Keywords:value-at-risk; average value-at-risk; linear regression; least-squares residuals; M-estimators; quantile regression; conditional risk measures; law-invariant risk measures; statistical inference PDFBibTeX XMLCite \textit{S. Y. Chun} et al., Oper. Res. 60, No. 4, 739--756 (2012; Zbl 1260.91121) Full Text: DOI Link