A concave optimization-based approach for sparse portfolio selection

References

• Bertsimas , D. and Shioda , R. 2009 . Algorithms for cardinality-constrained quadratic optimization . Comp. Optim. Appl , 43 : 1 – 22 .
   Web of Science ®Google Scholar
• Bienstock , D. 1996 . Computational study of a family of mixed-integer quadratic programming problems . Math. Program , 74 : 121 – 140 .
   Web of Science ®Google Scholar
• Black , F. and Litterman , R. 1991 . Asset allocation: Combining investor views with market equilibrium . J. Fixed Income , 1 : 7 – 18 .
   Google Scholar
• Bradley , P. S. and Mangasarian , O. L. 1998 . “ Feature selection via concave minimization and support vector machines ” . In Machine Learning Proceedings of the Fifteenth International Conference (ICML ’98) , Edited by: Shavlik , J. 82 – 90 . San Francisco, CA : Morgan Kaufmann .
   Google Scholar
• Broadie , M. 1993 . Computing efficient frontiers using estimated parameters . Ann. Oper. Res , 45 : 21 – 58 .
   Google Scholar
• Brodie , J. , Daubechies , I. , De Mol , C. , Giannone , D. and Loris , I. Sparse and stable Markovitz portfolios European Central Bank Working Paper Series, No. 36, 2008
   Google Scholar
• Cesarone , F. , Scozzari , A. and Tardella , F. Efficient algorithms for mean–variance portfolio optimization with hard real-world constraints, Giornale dell'Istituto Italiano degli Attuari LXXII (2009), pp. 37–56
   Google Scholar
• Chopra , V. K. 1993 . Improving optimization . J. Invest , 2 : 51 – 59 .
   Google Scholar
• Chopra , V. K. , Hensel , C. R. and Turner , A. L. 1993 . Massaging mean–variance inputs: Return from alternative investment strategies in the 1980s . Manag. Sci , 39 : 845 – 855 .
   Web of Science ®Google Scholar
• Chopra , V. K. and Ziemba , W. T. 1993 . The effect of errors in means, variances and covariances on optimal portfolio choice . J. Portfolio Manag , 19 : 6 – 11 .
   Web of Science ®Google Scholar
• DeMiguel , V. , Garlappi , L. , Nogales , F. J. and Uppal , R. 2009 . A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms . Manag. Sci , 55 ( 5 ) : 798 – 812 .
   Web of Science ®Google Scholar
• DeMiguel , V. and Nogales , F. J. 2009 . Portfolio selection with robust estimation . Oper. Res , 57 : 560 – 577 .
   Web of Science ®Google Scholar
• El Ghaoui , L. , Oks , M. and Oustry , F. 2003 . Worst-case value-at-risk and robust portfolio optimization: A conic programming approach . Oper. Res , 51 ( 4 ) : 543 – 556 .
   Web of Science ®Google Scholar
• Frank , M. and Wolfe , P. 1956 . An algorithm for quadratic programming . Naval Res. Logist. Quart , 3 : 95 – 110 .
   Google Scholar
• Grosso , A. , Locatelli , M. and Schoen , F. 2007 . A population based approach for hard global optimization problems based on dissimilarity measures . Math. Program , 110 : 373 – 404 .
   Web of Science ®Google Scholar
• Jagannathan , R. and Ma , T. 2003 . Risk reduction in large portfolios: Why imposing the wrong constraints helps . J. Finance , 58 : 1651 – 1684 .
   Web of Science ®Google Scholar
• Leary , R. H. 2000 . Global optimization on funneling landscapes . J. Global Optim , 18 : 367 – 383 .
   Web of Science ®Google Scholar
• Luenberger , D. G. 1998 . Investment Science , New York, NY : Oxford University Press .
   Google Scholar
• Mangasarian , O. L. 1996 . “ Machine learning via polyhedral concave minimization ” . In Applied Mathematics and Parallel Computing – Festschrift for Klaus Ritter , Edited by: Fischer , H. , Riedmueller , B. and Schaeffler , S. 175 – 188 . Germany : Physica-Verlag .
   Google Scholar
• Markovitz , H. M. 1952 . Portfolio selection . J. Finance , 7 : 77 – 91 .
   Web of Science ®Google Scholar
• Merton , R. C. 1980 . On estimating the expected return on the market: An exploratory investigation . J. Financ. Econ , 8 : 323 – 361 .
   Web of Science ®Google Scholar
• Michaud , R. O. 2001 . Efficient Asset Management: A Practical Guide to Stock Portfolio Management and Asset Allocation , New York, NY : Oxford University Press .
   Google Scholar
• F. Rinaldi, Concave programming for finding sparse solutions to problems with convex constraints, Tech. Rep. 1–8, Dipartimento di Informatica e Sistemistica, Sapienza Università di Roma, 2011, Optimization Methods and Software, in press
   Google Scholar
• Rinaldi , F. , Schoen , F. and Sciandrone , M. 2010 . Concave programming for minimizing the zero-norm over polyhedral sets . Comput. Optim. Appl , 46 : 467 – 486 .
   Web of Science ®Google Scholar
• Weston , J. , Elisseef , A. and Scholkopf , B. 2003 . Use of the zero-norm with linear models and kernel model . J. Mach. Learn. Res , 3 : 1439 – 1461 .
   Google Scholar