Portfolio Optimization with Nonparametric Value at Risk: A Block Coordinate Descent Method

References

• Alexander GJ, Baptista AM (2004) A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model. Management Sci. 50(9):1261–1273.Link, Google Scholar
• Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
• Benati S, Rizzi R (2007) A mixed integer linear programming formulation of the optimal mean/value-at-risk portfolio problem. Eur. J. Oper. Res. 176(1):423–434.Crossref, Google Scholar
• Bertsekas DP (1999) Nonlinear Programming (Athena Scientific, Belmont, MA).Google Scholar
• Bickel PJ (1967) Some contributions to the theory of order statistics. Proc. Fifth Berkeley Sympos. Math. Statist. Probab., Volume 1: Statist. (University California Press, Berkeley, CA).Google Scholar
• Bonami P, Lejeune MA (2009) An exact solution approach for portfolio optimization problems under stochastic and integer constraints. Oper. Res. 57(3):650–670.Link, Google Scholar
• Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Butler JS, Schachter B (1998) Estimating value-at-risk with a precision measure by combining kernel estimation with historical simulation. Rev. Deriv. Res. 1(4):371–390.Google Scholar
• Chang YP, Hung MC, Wu YF (2003) Nonparametric estimation for risk in value-at-risk estimator. Commun. Stat. Simul. Comput. 32(4):1041–1064.Crossref, Google Scholar
• Chen SX, Tang CY (2005) Nonparametric inference of value-at-risk for dependent financial returns. J. Financial Econom. 3(2):227–255.Crossref, Google Scholar
• Cheng MY, Peng L (2002) Regression modeling for nonparametric estimation of distribution and quantile functions. Stat. Sinica 12(12):1043–1060.Google Scholar
• Clarke FH (1983) Optimization and Nonsmooth Analysis (Wiley, New York).Google Scholar
• Cui XT, Zhu SS, Sun XL, Li D (2013) Nonlinear portfolio selection using approximate parametric value-at-risk. J. Banking Finance 37(6):2124–2139.Crossref, Google Scholar
• Duffie D, Pan J (1997) An overview of value at risk. J. Derivatives 4(3):7–49.Crossref, Google Scholar
• Gaivoronski AA, Pflug G (2005) Value at risk in portfolio optimization: Properties and computational approach. J. Risk 7(2):1–31.Crossref, Google Scholar
• Goldstein T, Osher S (2009) The split Bregman method for ℓ1-regularized problems. SIAM J. Imaging Sci. 2(2):323–343.Crossref, Google Scholar
• He BS, Tao M, Yuan XM (2012) Alternating direction method with Gaussian back substitution for separable convex programming. SIAM J. Optim. 22(2):313–340.Crossref, Google Scholar
• Heyde CC, Kou SG (2004) On the controversy over tailweight of distributions. Oper. Res. Lett. 32(5):399–408.Crossref, Google Scholar
• J. P. Morgan (1996) RiskMetrics™. Technical report, J. P. Morgan Company, New York.Google Scholar
• Jorion P (2007) Value at Risk: The New Benchmark for Managing Financial Risk (McGraw-Hill, New York).Google Scholar
• Kou S, Peng X, Heyde CC (2013) External risk measures and basel accords. Math. Oper. Res. 38(3):393–417.Link, Google Scholar
• Li Q, Racine JS (2007) Nonparametric Econometrics: Theory and Practice (Princeton University Press, Princeton, NJ).Google Scholar
• Lim AEB, Shanthikumar JG, Vahn GY (2011) Conditional value-at-risk in portfolio optimization: Coherent but fragile. Oper. Res. Lett. 39(3):163–171.Crossref, Google Scholar
• Linsmeier TJ, Pearson ND (2000) Value at risk. Financial Analysts J. 56(2):47–67.Crossref, Google Scholar
• Lobo MS, Vandenberghe L, Boyd S, Lebret H (1998) Applications of second-order cone programming. Linear Algebra Appl. 284(1–3):193–228.Crossref, Google Scholar
• Luedtke J (2014) A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Math. Programming 146(1–2):219–244.Crossref, Google Scholar
• Mausser H, Rosen D (1999) Beyond VaR: From measuring risk to managing risk. ALGO Res. Quart. 1:5–20.Google Scholar
• Parzen E (1979) Nonparametric statistical data modeling. J. Amer. Statist. Assoc. 74(365):105–121.Crossref, Google Scholar
• Qiu F, Ahmed S, Dey SS, Wolsey LA (2014) Covering linear programming with violations. INFORMS J. Comput. 26(3):531–546.Link, Google Scholar
• Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2(1):21–42.Crossref, Google Scholar
• Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.Crossref, Google Scholar
• Sheather SJ, Marron JS (1990) Kernel quantile estimators. J. Amer. Statist. Assoc. 85:410–416.Crossref, Google Scholar
• Shen Y, Wen ZW, Zhang Y (2014) Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization. Optim. Methods Softw. 29(2):239–263.Crossref, Google Scholar
• Wen ZW, Peng XH, Liu X, Bai XD, Sun XL (2013) Asset allocation under the Basel Accord risk measures. Technical report, http://www.optimization-online.org/DB_FILE/2013/01/3730.pdf.Google Scholar
• Xu YY, Yin WT, Wen ZW, Zhang Y (2012) An alternating direction algorithm for matrix completion with nonnegative factors. Front. Math. China 7(2):365–384.Crossref, Google Scholar
• Yang SS (1985) A smooth nonparametric estimator of a quantile function. J. Amer. Statist. Assoc. 80(392):1004–1011.Crossref, Google Scholar
• Yao HX, Li ZF, Lai YZ (2013) Mean-CVaR portfolio selection: A nonparametric estimation framework. Comput. Oper. Res. 40(4):1014–1022.Crossref, Google Scholar
• Yin W, Osher S, Goldfarb D, Darbon J (2008) Bregman iterative algorithms for ℓ1-minimization with applications to compressed sensing. SIAM J. Imaging Sci. 1(1):143–168.Crossref, Google Scholar
• Zhu SS, Ji XD, Li D (2015) A robust set-valued scenario approach for handling modeling risk in portfolio optimization. J. Comput. Finance 19(1):11–40.Crossref, Google Scholar