Skip to main content
SpringerLink
Log in

DC Programming and DCA for Portfolio Optimization with Linear and Fixed Transaction Costs

  • Conference paper
Book cover Intelligent Information and Database Systems (ACIIDS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8398))

Included in the following conference series:

Abstract

In this work, a single-period portfolio selection problem which consists of minimizing the total transaction cost subject to different types of constraints on feasible portfolios was considered. The total transaction cost function is separable and discontinuous. This problem is nonconvex and very hard to solve. First, by using additional binary variables, we transform it into a mixed zero-one program and then investigate a DC (Difference of Convex functions) programming framework for designing solution methods. Two approaches are developed: DCA (DC Algorithm) and a combination of DCA and Branch & Bound technique. Computational experiments are reported to demonstrate high efficiency and computational inexpensiveness of DCA, which provides good approximate global solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Le Thi, H.A.: DC Programming and DCA, http://lita.sciences.univ-metz.fr/~lethi

  2. Le Thi, H.A., Pham Dinh, T., Huynh, V.N.: Exact penalty and Error Bounds in DC programming. Journal of Global Optimization 52(3), 509–535 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kellerer, H., Mansini, R., Speranza, M.G.: Selecting Portfolios with Fixed Costs and Minimum Transaction Lots. Annals of Operations Research 99, 287–304 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Konno, H., Wijayanayake, A.: Mean-absolute deviation portfolio optimization model under transaction costs. Journal of the Operation Research Society of Japan 42(4), 422–435 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Konno, H., Wijayanayake, A.: Portfolio optimization problems under concave transaction costs and minimal transaction unit constraints. Mathematical Programming 89(B), 233–250 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Konno, H., Yamamoto, R.: Global Optimization Versus Integer Programming in Portfolio Optimization under Nonconvex Transaction Costs. Journal of Global Optimization 32, 207–219 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Le Thi, H.A.: Contribution à l’optimisation non convexe et l’optimisation globale: théorie, algorithmes et applications. Habilitation à Diriger de Recherches. Université de Rouen, France (1997)

    Google Scholar 

  8. Le Thi, H.A., Pham Dinh, T.: A continuous approach for globally solving linearly constrained quadratic zero-one programming problems. Optimization 45(1-2), 12–28 (2001)

    Google Scholar 

  9. Le Thi, H.A., Pham Dinh, T.: The DC (Difference of convex functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems. Annals of Operations Research 133, 23–46 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lobo, M.S., Fazel, M., Boyd, S.: Portfolio optimization with linear and fixed transaction costs. Annals of Operations Research 157, 341–365 (2007)

    Article  MathSciNet  Google Scholar 

  11. Markowitz, H.: Portfolio selection. The Journal of Finance 7(1), 77–91 (1952)

    Google Scholar 

  12. Pham Dinh, T., Le Thi, H.A.: 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) 22(1), 289–355 (1997)

    MATH  Google Scholar 

  13. Pham Dinh, T., Le Thi, H.A.: A d.c. optimazation algorithm for solving the trust region subproblem. SIAM Journal of Optimization 8(2), 476–505 (1998)

    Article  MATH  Google Scholar 

  14. Le Thi, H.A., Pham Dinh, T., Le, D.M.: Exact penalty in DC programming. Vietnam Journal of Mathematics 27(2), 169–178 (1999)

    MATH  MathSciNet  Google Scholar 

  15. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Mathematics, National Institute for Applied Sciences - Rouen, 76801, Saint Etienne du Rouvray, France

    Tao Pham Dinh

  2. Departement of Mathematics, Hanoi University of Agriculture, Trau Quy, Gia Lam, Ha Noi, Viet Nam

    Viet-Nga Pham

  3. Laboratory of Theorical and Applied Computer Science LITA EA 3097, University of Lorraine, Ile du Saulcy, Metz, 57045, France

    Hoai An Le Thi

Authors
  1. Tao Pham Dinh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Viet-Nga Pham
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hoai An Le Thi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Informatics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Ngoc Thanh Nguyen  & Bogdan Trawiński  & 

  2. Faculty of Engineering, Department of Computer Engineering, King Mongkut’s Institute of Technology Ladkrabang, 10520, Bangkok, Thailand

    Boonwat Attachoo

  3. Software Engineering Program, King Mongkut’s Institute of Technology Ladkrabang, 10520, Bangkok, Thailand

    Kulwadee Somboonviwat

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Pham Dinh, T., Pham, VN., Le Thi, H.A. (2014). DC Programming and DCA for Portfolio Optimization with Linear and Fixed Transaction Costs. In: Nguyen, N.T., Attachoo, B., Trawiński, B., Somboonviwat, K. (eds) Intelligent Information and Database Systems. ACIIDS 2014. Lecture Notes in Computer Science(), vol 8398. Springer, Cham. https://doi.org/10.1007/978-3-319-05458-2_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-05458-2_41

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05457-5

  • Online ISBN: 978-3-319-05458-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation