IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v28y2011i01ns0217595911003041.html
   My bibliography  Save this article

On Dual Approaches To Efficient Optimization Of Lp Computable Risk Measures For Portfolio Selection

Author

Listed:
  • WŁODZIMIERZ OGRYCZAK

    () (Institute of Control & Computation Engineering, Warsaw University of Technology, 00-665 Warsaw, Poland)

  • TOMASZ ŚLIWIŃSKI

    (Institute of Control & Computation Engineering, Warsaw University of Technology, 00-665 Warsaw, Poland)

Abstract

In the original Markowitz model for portfolio optimization the risk is measured by the variance. Several polyhedral risk measures have been introduced leading to Linear Programming (LP) computable portfolio optimization models in the case of discrete random variables represented by their realizations under specified scenarios. The LP models typically contain the number of constraints (matrix rows) proportional to the number of scenarios while the number of variables (matrix columns) proportional to the total of the number of scenarios and the number of instruments. They can effectively be solved with general purpose LP solvers provided that the number of scenarios is limited. However, real-life financial decisions are usually based on more advanced simulation models employed for scenario generation where one may get several thousands scenarios. This may lead to the LP models with huge number of variables and constraints thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by alternative models taking advantages of the LP duality. In the introduced models the number of structural constraints (matrix rows) is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability.

Suggested Citation

  • Włodzimierz Ogryczak & Tomasz Śliwiński, 2011. "On Dual Approaches To Efficient Optimization Of Lp Computable Risk Measures For Portfolio Selection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 28(01), pages 41-63.
  • Handle: RePEc:wsi:apjorx:v:28:y:2011:i:01:n:s0217595911003041
    DOI: 10.1142/S0217595911003041
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595911003041
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel Espinoza & Eduardo Moreno, 2014. "A primal-dual aggregation algorithm for minimizing conditional value-at-risk in linear programs," Computational Optimization and Applications, Springer, vol. 59(3), pages 617-638, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:apjorx:v:28:y:2011:i:01:n:s0217595911003041. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tai Tone Lim). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.