Long-Short Portfolio Optimization Under Cardinality Constraints by Difference of Convex Functions Algorithm

Journal of Optimization Theory and Applications

Volumn 161, Issue 1, 2014, Pages 199-224

  Le Thi, Hoai An ^a   Moeini, Mahdi ^b  

^a UNIVERSITÉ DE LORRAINE   (France)

^b TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

Cardinality constraints; Complementarity constraints; DC programming; DCA; Mixed integer programming; Portfolio selection; Threshold constraints

Indexed keywords

BENCHMARKING; CONVEX OPTIMIZATION; FINANCIAL DATA PROCESSING; INTEGER PROGRAMMING;

CARDINALITY CONSTRAINTS; COMPLEMENTARITY CONSTRAINT; CONSTRAINT LIMITS; D.C. PROGRAMMING; DC ALGORITHM; DC PROGRAMMING; DIFFERENCE OF CONVEX FUNCTIONS; MIXED-INTEGER PROGRAMMING; PORTFOLIO SELECTION; THRESHOLD CONSTRAINTS;

FUNCTIONS;

EID: 84898490238     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-012-0197-0     Document Type: Article

References (28)

1. Markowitz, H. M.: Portfolio selection. J. Finance 7(1), 77-91 (1952).
2. Markowitz, H. M.: Portfolio Selection. Wiley, New York (1959).
3. Bartholomew-Biggs, M.: Nonlinear Optimization with Financial Applications. Kluwer Academic, Norwell (2005).
4. Elton, E. J., Grubner, M. J., Brown, S. J., Goetzmann, W. N.: Modern Portfolio Theory and Investment Analysis. Wiley, New York (2003).
5. Fernandez, A., Gomez, S.: Portfolio selection using neural networks. Comput. Oper. Res. 34, 1177-1191 (2007).
6. Konno, H., Yamazaki, H.: Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manag. Sci. 37, 519-531 (1991).
7. Ogryczak, W., Ruszczynski, A.: From stochastic dominance to mean-risk model: semi-deviations as risk measures. Eur. J. Oper. Res. 116, 33-50 (1999).
8. Ogryczak, W., Ruszczynski, A.: On consistency of stochastic dominance and mean-semi deviation models. Math. Program. 89, 217-232 (2001).
9. Chang, T. J., Meade, N., Beasley, J. E., Sharaiha, Y. M.: Heuristics for cardinality constrained portfolio optimization. Comput. Oper. Res. 27, 1271-1302 (2000).
10. Jobst, N., Horniman, M., Lucas, C., Mitra, G.: Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints. Quant. Finance 1, 1-13 (2001).
11. Le Thi, H. A., Moeini, M., Pham Dinh, T.: Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA. Comput. Manag. Sci. 6(4), 477-501 (2009).
12. Konno, H., Akishino, K., Yamamoto, R.: Optimization of a long-short portfolio under nonconvex transaction cost. Comput. Optim. Appl. 32, 115-132 (2005).
13. Konno, H., Koshizuka, T., Yamamoto, R.: Mean-variance portfolio optimization problems under short sale opportunity. Dyn. Contin. Discrete Impuls. Syst., 12(4), 483-498 (2005).
14. DC Programming and DCA: http://lita. sciences. univ-metz. fr/~lethi.
15. Konno, H., Wijayanayake, A.: Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Math. Program., Ser. B 89, 233-250 (2001).
16. Konno, H., Wijayanayake, A.: Portfolio optimization under DC transaction costs and minimal transaction unit constraints. J. Glob. Optim. 22, 137-154 (2002).
17. Konno, H., Yamamoto, R.: Global optimization versus integer programming in portfolio optimization under nonconvex transaction costs. J. Glob. Optim. 32, 207-219 (2005).
18. Konno, H., Yamamoto, R.: Integer programming approaches in mean-risk models. Comput. Manag. Sci. 2, 339-351 (2005).
19. Konno, H.: Applications of global optimization to portfolio analysis. In: Audet, C., Hansen, P., Savard, G. (eds.) Essays and Surveys in Global Optimization, 1st edn., pp. 195-210. Springer, Berlin (2005).
20. Le Thi, H. A., Moeini, M., Pham Dinh, T.: DC programming approach for portfolio optimization under step increasing transaction costs. Optimization 58(3), 267-289 (2009).
21. Le Thi, H. A., Pham Dinh, T., Muu, L. D.: Exact penalty in DC programming. Vietnam J. Math. 27, 169-178 (1999).
22. Rockafellar, R. T.: Convex Analysis. Princeton University Press, Princeton (1970).
23. Le Thi, H. A., Pham Dinh, T.: A continuous approach for globally solving linearly constrained quadratic zero-one programming problems. Optimization 50(1-2), 93-120 (2001).
24. Le Thi, H. A., Pham Dinh, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world non convex optimization problems. Ann. Oper. Res. 133, 23-46 (2005).
25. Pham Dinh, T., Le Thi, H. A.: In: Convex Analysis Approach to D. C. Programming: Theory, Algorithms and Applications, Acta Mathematica Vietnamica, Dedicated to Professor Hoang Tuy on the Occasion of his 70th Birthday, vol. 22, pp. 289-355 (1997).
26. Le Thi, H. A.: Contribution à l'optimisation non convexe et l'optimisation globale: théorie, algorithmes et applications. Habilitation à Diriger des, Recherches, Université de Rouen (1997).
27. Pham Dinh, T., Le Thi, H. A.: DC optimization algorithms for solving the trust region subproblem. SIAM J. Optim. 8, 476-505 (1998).
28. Canakgoz, N. A., Beasley, J. E.: Mixed-integer programming approaches for index tracking and enhanced indexation. Eur. J. Oper. Res. 196, 384-399 (2009).