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Nonparametric Inference for VaR, CTE, and Expectile with High-Order Precision

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References

  • Ahn, J. Y., and N. D. Shyamalkumar. 2014. Asymptotic Theory for the Empirical Haezendonck–Goovaerts Risk Measure. Insurance: Mathematics and Economics 55:78–90.
  • Bakar, S. A. A., N. A. Hamzah, M. Maghsoudi, and S. Nadarajah. 2015. Modeling Loss Data Using Composite Models. Insurance: Mathematics and Economics 61:146–154.
  • Baysal, R. E., and J. Staum. 2008. Empirical Likelihood for Value-at-Risk and Expected Shortfall. Journal of Risk 11(1):3–33.
  • Bellini, F., B. Klar, A. Müller, and E. R. Gianin. 2014. Generalized Quantiles as Risk Measures. Insurance: Mathematics and Economics 54:41–48.
  • Chen, J., A. M. Variyath, and B. Abraham. 2008. Adjusted Empirical Likelihood and Its Properties. Journal of Computational and Graphical Statistics 17(2):426–443.
  • Chen., S. X. Nonparametric Estimation of Expected Shortfall. 2007. Journal of Financial Econometrics 6(1):87–107.
  • Chen, S. X., and H. Cui. 2006. On Bartlett Correction of Empirical Likelihood in the Presence of Nuisance Parameters. Biometrika 93(1):215–220.
  • Chen, S. X., and P. Hall. 1993. Smoothed Empirical Likelihood Confidence Intervals for Quantiles. Annals of Statistics 21(3):1166–1181.
  • Chen, S. X. and C. Y. Tang. 2005. Nonparametric Inference of Value-at-Risk for Dependent Financial Returns. Journal of Financial Econometrics 3(2):227–255.
  • Cooray, K., and M. M. A. Ananda. 2005. Modeling Actuarial Data with a Composite Lognormal-Pareto Model. Scandinavian Actuarial Journal 2005(5):321–334.
  • DiCiccio, T., P. Hall, J. Romano, et al. 1991. Empirical Likelihood is Bartlett-Correctable. Annals of Statistics 19(2):1053–1061.
  • Hall, P., and B. La Scala. 1990. Methodology and Algorithms of Empirical Likelihood. International Statistical Review/Revue Internationale de Statistique 58(2):109–127.
  • Hardy, M. R. 2000. Hedging and Reserving for Single-Premium Segregated Fund Contracts. North American Actuarial Journal 4(2):63–74.
  • B. John Manistre, and G. H Hancock. 2005. Variance of the Cte Estimator. North American Actuarial Journal 9(2):129–156.
  • Jones, B. L., and R. Zitikis. 2003. Empirical Estimation of Risk Measures and Related Quantities. North American Actuarial Journal 7(4):44–54.
  • Kim, J. H. T. and M. R. Hardy. 2009. Estimating the Variance of Bootstrapped Risk Measures. ASTIN Bulletin 39(1):199–223.
  • Kou, S., X. Peng, and C. C. Heyde. 2013. External Risk Measures and Basel Accords. Mathematics of Operations Research 38(3):393–417.
  • Krätschmer, V., A. Schied, and H. Zähle. 2014. Comparative and Qualitative Robustness for Law-Invariant Risk Measures. Finance and Stochastics 18(2):271–295.
  • Liu, Y., and J. Chen. 2010. Adjusted Empirical Likelihood with High-Order Precision. Annals of Statistics 38(3):1341–1362.
  • McNeil, A. J. 1997. Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory. ASTIN Bulletin 27(1):117–137.
  • Nadarajah, S. and S. A. A. Bakar. 2014. New Composite Models for the Danish Fire Insurance Data. Scandinavian Actuarial Journal 2014(2):180–187.
  • Newey, W. K. and J. L. Powell. 1987. Asymmetric Least Squares Estimation and Testing. Econometrica: Journal of the Econometric Society 55(4):819–847.
  • Owen, A. B. 1988. Empirical Likelihood Ratio Confidence Intervals for a Single Functional. Biometrika 75 (2):237–249.
  • Owen, A. B. 1990. Empirical Likelihood Ratio Confidence Regions. Annals of Statistics 18(1):90–120.
  • Owen, A. B. 2001. Empirical Likelihood. New York: Chapman and Hall/CRC.
  • Peng, L., Y. Qi, R. Wang, and J. Yang. 2012. Jackknife Empirical Likelihood Method for Some Risk Measures and Related Quantities. Insurance: Mathematics and Economics 51(1):142–150.
  • Peng, L., X. Wang, and Y. Zheng. 2015. Empirical Likelihood Inference for Haezendonck-Goovaerts Risk Measure. European Actuarial Journal 5(2):427–445.
  • Qin, J. and J. Lawless. 1994. Empirical Likelihood and General Estimating Equations. Annals of Statistics 22(1):300–325.
  • Scollnik, D. P. M., and C. Sun. 2012. Modeling with Weibull-Pareto Models. North American Actuarial Journal 16(2):260–272.
  • Tan, K. S., and C. Weng. 2014. Empirical Approach for Optimal Reinsurance Design. North American Actuarial Journal 18(2):315–342.
  • Wang, X., and L. Peng. 2016. Inference for Intermediate Haezendonck–Goovaerts Risk Measure. Insurance: Mathematics and Economics 68:231–240.
  • Wang, X., Q. Liu, Y. Hou, and L. Peng. 2018. Nonparametric Inference for Sensitivity of Haezendonck–Goovaerts Risk Measure. Scandinavian Actuarial Journal 2018(8):661–680.
  • Yamai, Y., and T. Yoshiba. 2002. Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization. Monetary and Economic Studies 20(1):87–121.
  • Zhou, M., and Y. Yang. 2016. Emplik: Empirical Likelihood Ratio for Censored/Truncated Data. R package version 1.0-3. Vienne: R Founndation.
  • Ziegel., J. F. 2016. Coherence and Elicitability. Mathematical Finance 26(4):901–918.

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