Expected shortfall estimation for apparently infinite-mean models of operational risk

References

• Balkema, A.A. and De Haan, L., Residual life time at great age. Ann. Probab., 1974, 5, 792–804.
   Web of Science ®Google Scholar
• Basel Committee on Banking Supervision (BCBS), Principles for the sound management of operational risk. Technical Report, 2011a. Available online at: http://www.bis.org/publ/bcbs195.pdf.
   Google Scholar
• Basel Committee on Banking Supervision (BCBS), Operational risk -- Supervisory guidelines for the advanced measurement approaches. Technical Report, 2011b. Available online at: http://www.bis.org/publ/bcbs196.pdf.
   Google Scholar
• Basel Committee on Banking Supervision (BCBS), Review of the principles for the sound management of operational risk. Technical Report, 2014. Available online at: http://www.bis.org/publ/bcbs292.pdf.
   Google Scholar
• Beirlant, J., Fraga Alves, M.I., Gomes, M.I. and Meerschaert, M.M., Extreme value statistics for truncated Pareto-type distributions, arXiv:1410.4097v3, 2014.
   Google Scholar
• Böcker, K. and Klüppelberg, C., Multivariate models for operational risk. Quant. Finance, 2010, 10, 855–869.
   Web of Science ®Google Scholar
• Chavez-Demoulin, V., Embrechts, P. and Ne\xu{s}lehov{\’a}, J., Quantitative models for operational risk: Extremes, dependence and aggregation. J. Bank. Financ., 2006, 30, 2635–2658.
   Web of Science ®Google Scholar
• Chavez-Demoulin, V., Embrechts, P. and Hofert, M., An extreme value approach for modeling operational risk losses depending on covariates. J. Risk Insur., 2015, doi:10.1111/jori.12059.
   Web of Science ®Google Scholar
• Cirillo, P., Are your data really Pareto distributed? Phys. A: Stat. Mech. Appl., 2013, 392, 5947–5962.
   Web of Science ®Google Scholar
• Clauset, A., Shalizi, C.R. and Newman, M.E.J., Power-law distributions in empirical data. SIAM Rev., 2009, 51, 661–703.
   Web of Science ®Google Scholar
• de Fontnouvelle, P., Results of the operational risk loss data collection exercise (LDCE) and quantitative impact study (QIS). Presentation at implementing an AMA to operational risk, Federal Reserve Bank of Boston, 2005. Available online at: http://www.bos.frb.org/bankinfo/conevent/oprisk2005.
   Google Scholar
• de Fontnouvelle, P., DeJesus-Rueff, V., Jordan, J. and Rosengren, E., Capital and risk: New evidence on implications of large operational risk losses. Federal Reserve Board of Boston Working Paper, 2003.
   Google Scholar
• de Fontnouvelle, P., Rosengren, E. and Jordan, J., Implications of alternative operational risk modeling techniques. Working Paper 11103, 2005. doi:10.3386/w11103.
   Google Scholar
• de Haan, L. and Ferreira, A., Extreme Value Theory: An Introduction, 2006 (Springer: Berlin).
   Google Scholar
• Embrechts, P., Klüppelberg, C. and Mikosch, T., Modelling Extremal Events, 2003 (Springer: Berlin).
   Google Scholar
• Falk, M., Hüsler, J. and Reiss, R.D., Laws of Small Numbers: Extremes and Rare Events, 2004 (Birkhäuser: Basel).
   Google Scholar
• Fiordelisi, F., Soana, M.-G. and Schwizer, P., Reputational losses and operational risk in banking. Eur. J. Finance, 2014, 20, 105–124.
   Web of Science ®Google Scholar
• Gnedenko, D.V., Sur la distribution limité du terme d’une série aléatoire. Ann. Math., 1943, 44, 423–453.
   Web of Science ®Google Scholar
• Gumbel, E.J., Statistics of Extremes, 1958 (Cambridge University Press: Cambridge).
   Google Scholar
• Hull, J.C., Risk Management and Financial Insitutions, 2015 (Wiley: New York).
   Google Scholar
• Inmaculada, B.A., Meerschaert, M.M. and Panorska, A.K., Parameter estimation for the truncated Pareto distribution. J. Am. Stat. Assoc., 2006, 101, 270–277.
   Web of Science ®Google Scholar
• Kleiber, C. and Kotz, S., Statistical Size Distributions in Economics and Actuarial Sciences, 2003 (Wiley: New York).
   Google Scholar
• Mandelbrot, B. and Hudson, R., The (Mis)Behavior of Markets, 2004 (Basic Books: New York).
   Google Scholar
• Maronna, R., Martin, R.D. and Yohai, V., Robust Statistics -- Theory and Methods, 2006 (Wiley: New York).
   Google Scholar
• McNeil, A., Rüdiger, F. and Embrechts, P., Quantitative Risk Management: Concepts, Techniques and Tools, 2015 (Princeton University Press: Princeton, NJ).
   Google Scholar
• Moscadelli, M., The modelling of operational risk: Experience with the analysis of the data collected by the Basel committee. Technical Report 517, Banca d’Italia, 2004.
   Google Scholar
• Nes̆lehová, J., Embrechts, P. and Chavez-Demoulin, V., Infinite-mean models and the LDA for operational risk. J. Oper. Risk 2006, 1, 3–25.
   Web of Science ®Google Scholar
• Peters, G.W. and Shevchenko, P.V., Advances in Heavy-Tailed Risk Modeling, A Handbook of Operational Risk, 2015 (Wiley: New York).
   Google Scholar
• Pickands, J. III, Statistical inference using extreme order statistics. Ann. Stat., 1975, 3, 119–131.
   Web of Science ®Google Scholar
• Puccetti, G. and Rüschendorf, L., Asymptotic equivalence of conservative value-at-risk- and expected shortfall-based capital charges. J. Risk, 2014, 16(3), 3–22.
   Web of Science ®Google Scholar
• Reiss, R. and Thomas, M., Statistical Analysis of Extreme Values, 2001 (Birkhäuser: Basel).
   Google Scholar
• Ruckdeschel, P. and Horbenko, N., Optimally robust estimators in generalized Pareto models. Statistics, 2013, 47, 762–791.
   Web of Science ®Google Scholar
• Shao, J., Mathematical Statistics, 2008 (Springer: New York).
   Google Scholar
• Taleb, N.N., Dynamic Hedging, 1997 (Wiley: New York).
   Google Scholar
• Taleb, N.N. and Douady, R., Mathematical definition, mapping, and detection of (anti)fragility. Quant. Finance, 2013, 13, 1677–1689.
   Web of Science ®Google Scholar
• Tursunalieva, A. and Silvapulle, P., A semi-parametric approach to estimating the operational risk and expected shortfall. Appl. Econ., 2014, 46, 3659–3672.
   Web of Science ®Google Scholar
• Weitzman, M.L., On modeling and intepreting the economics of catastrophic climate change. Rev. Econ. Stat., 2009, 1, 1–19.
   Web of Science ®Google Scholar