DC programming approach for portfolio optimization under step increasing transaction costs

Optimization

Volumn 58, Issue 3, 2009, Pages 267-289

  Le Thi, Hoai An ^a   Moeini, Mahdi ^a   Dinh, Tao Pham ^b  

^a UNIVERSITÉ DE LORRAINE   (France)

^b UNIVERSITÉ ET INSA DE ROUEN   (France)

Author keywords

Branch and bound; DC programming; DCA; Portfolio selection; Step increasing transaction cost function

Indexed keywords

EID: 70449396212     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331930902741721     Document Type: Article

References (25)

1. M.H.A. Davis and A.R. Norman, Portfolio selection with transaction costs, Math. Oper. Res. 15(4) (1990), pp. 676-713.
2. J.E. Harrington, et al., Collusive game solutions via optimisation, Math. Program. Ser. B 104(1-2) (2005), pp. 407-435.
3. J.B. Hiriart Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms, Springer, Berlin, 1993.
4. H. Konno, Applications of global optimization to portfolio analysis, in Essays and Surveys in Global Optimization, 1st ed., C. Audet, P. Hansen, and G. Savard, eds., Springer, USA, 2005, pp. 195-210.
5. H. Konno and A. Wijayanayake, Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints, Math. Program. Ser. B 89 (2001), pp. 233-250.
6. H. Konno and A. Wijayanayake, Portfolio optimization under DC transaction costs and minimal transaction unit constraints, J. Global Optimiz. 22 (2002), pp. 137-154.
7. H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Manag. Sci. 37 (1991), pp. 519-531.
8. H. Konno and R. Yamamoto, Global optimization versus integer programming in portfolio optimization under nonconvex transaction costs, J. Global Optim. 32 (2005), pp. 207-219.
9. H. Konno and R. Yamamoto, Integer programming approaches in mean-risk models, Comput. Manag. Sci. 2 (2005), pp. 339-351.
10. P.J. Laurent, Approximation et Optimisation, Kluwer Academic Publishers, Dordrecht, 1995.
11. H.A. Le Thi, Contribution á l'optimisation non convexe et l'optimisation globale: Théorie Algorithmes et Applications Habilitation á Diriger des Recherches, Universite de Rouen, France, 1997.
12. H.A. Le Thi and T. Pham Dinh, The DC (difference of convex functions) programming and DCA revisited with DC models of real world non convex optimization problems, Ann. Oper. Res. 133 (2005), pp. 23-46.
13. M.S. Lobo, M. Fazel, and S. Boyd, Portfolio optimization with linear and fixed transaction costs, Annal. Oper. Res. 152(1) (2007), pp. 341-365.
14. H. Markowitz, Portfolio Selection; Efficient Diversification of Investment, 1st ed., John Wiley and Sons, New York, 1959.
15. D. Maringer, Portfolio Management with Heuristic Optimization, Springer, Dordrecht, 2005.
16. W. Ogryczak and A. Ruszczynski, From stochastic dominance to mean-risk model: Semi- deviationas the risk measures, Europ. J. Oper. Res. 116 (1999), pp. 33-50.
17. W. Ogryczak and A. Ruszczynski, On consistency of stochastic dominance and mean-semi deviation models, Math. Prog. 89 (2001), pp. 217-232.
18. T. Pham Dinh and H.A Le Thi, Convex analysis approach to DC programming: Theory algorithms and applications, Acta Math. Vietnam. (dedicated to Professor Hoang Tuy on the occasion of his 70th birthday), 22(1) (1997), pp. 289-355.
19. T. Pham Dinh and H.A Le Thi, DC optimization algorithms for solving the trust region subproblem, SIAM J. Optim. 8 (1998), pp. 476-505.
20. T.Q. Phong, H.A. Le Thi, and T. Pham Dinh, Decomposition branch and bound method for globally solving linearly constrained indefinite quadratic minimization problems, Oper. Res. Lett. 17 (1995), pp. 215-220.
21. R.T. Rockafellar, Convex Analysis, 1st ed., Princeton University Press, Princeton, 1970.
22. C. Schnorr, T. Schule, and S. Weber, Variational reconstruction with DC-programming, in Advances in Discrete Tomography and its Applications, G.T. Herman and A. Kuba, eds., Birkhauser, Boston, 2007, pp. 227-243.
23. T. Schule, et al., Discrete tomography by convex-concave regularization and D.C. programming, Discr. Appl. Math. 151 (2005), pp. 229-243.
24. H. Tuy, Convex Analysis and Global Optimization, Kluwer Academic Publishers, Dortrecht, 1998.
25. H.G. Xue, C.X. Xu, and Z.X. Feng, Mean-variance portfolio optimal problem under concave transaction cost, Appl. Math. Comput. 174 (2006), pp. 1-12.