Conditional Value-at-Risk Approximation to Value-at-Risk Constrained Programs: A Remedy via Monte Carlo

Published Online:https://doi.org/10.1287/ijoc.2013.0572

References

  • Alexander GJ, Baptista AM (2004) A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model. Management Sci. 50:1261–1273.LinkGoogle Scholar
  • Alexander S, Coleman TF, Li Y (2006) Minimizing CVaR and VaR for a portfolio of derivatives. J. Bank Finance 30:583–605.CrossrefGoogle Scholar
  • Andersson F, Mausser H, Rosen D, Uryasev S (2001) Credit risk optimization with conditional value-at-risk criterion. Math. Programming 89:273–291.CrossrefGoogle Scholar
  • Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.CrossrefGoogle Scholar
  • Basova HG, Rockafellar RT, Royset JO (2011) A computational study of the buffered failure probability in reliability-based design optimization. Proc. 11th Conf. Appl. Statist. Probab. Civil Engrg., Zurich, Switzerland.CrossrefGoogle Scholar
  • Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math. Programming 88:411–424.CrossrefGoogle Scholar
  • Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization, Princeton Series in Applied Mathematics (Princeton University Press, Englewood Cliffs, NJ).CrossrefGoogle Scholar
  • Charnes A, Cooper WW, Symonds GH (1958) Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil. Management Sci. 4:235–263.LinkGoogle Scholar
  • Chen W, Sim M, Sun J, Teo C-P (2010) From CVaR to uncertainty set: Implications in joint chance-constrained optimization. Oper. Res. 58:470–485.LinkGoogle Scholar
  • Chu F, Nakayama MK (2012) Confidence intervals for quantiles when applying variance-reduction techniques. ACM Trans. Modeling Comput. Simulation 22(2):article 10.CrossrefGoogle Scholar
  • Chung H, Polak E, Sastry S (2010) On the use of outer approximations as an external active set strategy. J. Optim. Theory Appl. 146:51–75.CrossrefGoogle Scholar
  • Duffie D, Pan J (1997) An overview of value at risk. J. Derivatives 4:7–49.CrossrefGoogle Scholar
  • El Ghaoui L, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. 51:543–556.LinkGoogle Scholar
  • Gaivoronski A, Pflug G (2005) Value at risk in portfolio optimization: Properties and computational approach. J. Risk 7:1–31.CrossrefGoogle Scholar
  • Gupton GM, Finger CC, Bhatia M (1997) CreditMetrics™—Technical document (J.P. Morgan & Co., New York).Google Scholar
  • Hong LJ, Liu G (2009) Simulating sensitivities of conditional value at risk. Management Sci. 55:281–293.LinkGoogle Scholar
  • Hong LJ, Yang Y, Zhang L (2011) Sequential convex approximations to joint chance constrained programs: A Monte Carlo approach. Oper. Res. 59:617–630.LinkGoogle Scholar
  • Hu Z, Hong LJ, Zhang L (2013) A smooth Monte Carlo approach to joint chance constrained program. IIE Trans. 45:716–735.CrossrefGoogle Scholar
  • Iyengar G, Ma AKC (2013) Fast gradient descent method for mean-CVaR optimization. Ann. Oper. Res. 205:203–212.CrossrefGoogle Scholar
  • Jorion P (2010) Financial Risk Manager Handbook, Sixth ed. (Wiley, New York).Google Scholar
  • Krokhmal P, Palmquist J, Uryasev S (2002) Portfolio optimization with conditional value-at-risk objective and constraints. J. Risk 4:11–27.Google Scholar
  • Lim C, Sherali HD, Uryasev S (2010) Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization. Computational Optim. Appl. 46:391–415.CrossrefGoogle Scholar
  • Nemirovski A (2012) On safe tractable approximations of chance constraints. Eur. J. Oper. Res. 219:707–718.CrossrefGoogle Scholar
  • Nemirovski A, Shapiro A (2006) Convex approximations of chance constrained programs. SIAM J. Optim. 17:969–996.CrossrefGoogle Scholar
  • Ogryczak W, Śliwiński T (2011) On solving the dual for portfolio selection by optimizing conditional value at risk. Computational Optim. Appl. 50:591–595.CrossrefGoogle Scholar
  • Pagnoncelli BK, Ahmed S, Shapiro A (2009) Sample average approximation method for chance constrained programming: Theory and applications. J. Optim. Theory Appl. 142:399–416.CrossrefGoogle Scholar
  • Prékopa A (2003) Probabilistic programming. Ruszczynski A, Shapiro A, eds. Operations Research and Management Science: Stochastic Programming, Vol. 10 (Elsevier Science, Amsterdam), 267–352.CrossrefGoogle Scholar
  • Rockafellar RT, Royset JO (2010) On buffered failure probability in design and optimization of structures. Reliability Engrg. System Safety 95:499–510.CrossrefGoogle Scholar
  • Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2:21–41.CrossrefGoogle Scholar
  • Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26:1443–1471.CrossrefGoogle Scholar
  • Serfling RJ (1980) Approximation Theorems of Mathematical Statistics (Wiley, New York).CrossrefGoogle Scholar
  • Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Trindade AA, Uryasev S, Shapiro A, Zrazhevsky G (2007) Financial prediction with constrained tail risk. J. Banking Finance 31: 3524–3538.CrossrefGoogle Scholar
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