Simulating Sensitivities of Conditional Value at Risk

References

• Artzner P., Delbaen F., Eber J.-M., Heath D. Coherent measures of risk. Math. Finance (1999) 9(3):203–228Crossref, Google Scholar
• Bernhard P., Rapaport A. On a theorem of Danskin with an application to a theorem of Von Neumann-Sion. Nonlinear Anal., Theory, Methods Appl. (1995) 24:1163–1181Crossref, Google Scholar
• Broadie M., Glasserman P. Estimating security price derivatives using simulation. Management Sci. (1996) 42(2):269–285Link, Google Scholar
• Chambers J. M., Mallows C. L., Stuck B. W. A method for simulating stable random variables. J. Amer. Statist. Assoc. (1976) 71:340–344Crossref, Google Scholar
• Daníelsson J., Jorgensen B. N., Samorodnitsky G., Sarma M., de Vries C. G. Subadditivity re-examined: The case of value-at-risk. (2005) . Preprint, London School of Economics, LondonGoogle Scholar
• David H.Order Statistics (1981) 2nd ed.(Wiley, New York) Google Scholar
• Durrett R.Probability: Theory and Examples (1996) 2nd ed.(Duxbury Press, Belmont, CA) Google Scholar
• Fox B. L., Glynn P. W. Replication schemes for limiting expectations. Probab. Engrg. Inform. Sci. (1989) 3:299–318Crossref, Google Scholar
• Fu M. C., Henderson S. G., Nelson B. L. Gradient estimation. Handbooks in Operations Research and Management Science: Simulation (2006) (Elsevier, Amsterdam) 575–612Google Scholar
• Glasserman P.Gradient Estimation via Perturbation Analysis (1991) (Kluwer Academic Publishers, Norwell, MA) Google Scholar
• Glasserman P.Monte Carlo Methods in Financial Engineering (2004) (Springer, New York) Crossref, Google Scholar
• Glynn P. W. Likelihood ratio gradient estimation for stochastic systems. Comm. ACM (1990) 33:75–84Crossref, Google Scholar
• Heyde C. C., Kou S. G. On the controversy over tailweight of distributions. Oper. Res. Lett. (2004) 32:399–408Crossref, Google Scholar
• Heyde C. C., Kou S. G., Peng X. H. What is a good external risk measure: Bridging the gaps between robustness, subadditivity, and insurance risk measures. (2007) . Working paper, Department of Industrial Engineering and Operations Research, Columbia University, New YorkGoogle Scholar
• Hong L. J. Estimating quantile sensitivities. Oper. Res. (2008) . ePub ahead of print September 17, http://or.journal.informs.org/cgi/content/abstract/opre.1080.0531v1Google Scholar
• Hong L. J., Qi X. Stochastic linear programming and value-at-risk: An efficient Monte-Carlo approach. (2007) . Technical report, Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Hong KongGoogle Scholar
• Krokhmal P., Palmquist J., Uryasev S. Portfolio optimization with conditional value-at-risk objective and constraints. J. Risk (2002) 4:11–27Google Scholar
• Law A. M., Kelton W. D.Simulation Modeling and Analysis (2000) 3rd ed.(McGraw-Hill, Boston) Google Scholar
• Lehmann E. L.Elements of Large-Sample Theory (1999) (Springer-Verlag, New York) Crossref, Google Scholar
• Nocedal J., Wright S. J.Numerical Optimization (1999) (Springer-Verlag, New York) Crossref, Google Scholar
• Nolan J. P.Stable Distributions—Models for Heavy Tailed Data (2007) (Birkhäuser, Boston) Google Scholar
• Pflug G., Uryasev S. Some remarks on the value-at-risk and the conditional value-at-risk. Probabilistic Constrained Optimization: Methodology and Applications (2000) (Kluwer, Dordrecht, The Netherlands) 272–281Crossref, Google Scholar
• Rockafellar R. T., Uryasev S. Optimization of conditional value-at-risk. J. Risk (2000) 2:21–41Crossref, Google Scholar
• Rockafellar R. T., Uryasev S. Conditional value-at-risk for general loss distributions. J. Banking Finance (2002) 26:1443–1471Crossref, Google Scholar
• Rudin W.Real and Complex Analysis (1987) 3rd ed.(McGraw-Hill, Singapore) Google Scholar
• Ruszczyński A., Shapiro A. Optimization of convex risk functions. Math. Oper. Res. (2006) 31:433–452Link, Google Scholar
• Scaillet O. Nonparametric estimation and sensitivity analysis of expected shortfall. Math. Finance (2004) 14:115–129Crossref, Google Scholar
• Serfling R. J.Approximation Theorems of Mathematical Statistics (1980) (Wiley, New York) Crossref, Google Scholar
• Trindade A. A., Uryasev S., Shapiro A., Zrazhevsky G. Financial prediction with constrained tail risk. J. Banking Finance (2007) 31:3524–3538Crossref, Google Scholar