IDEAS home Printed from
   My bibliography  Save this paper

Multiobjective Lagrangian duality for portfolio optimization with risk measures


  • Elisa Pagani

    () (Department of Economics (University of Verona))


In this paper we present an application for a multiobjective optimization problem. The objective functions of the primal problem are the risk and the expected pain associated to a portfolio vector. Then, we present a Lagrangian dual problem for it. In order to formulate this problem, we introduce the theory about risk measures for a vector of random variables. The definition of this kind of measures is a very evolving topic; moreover, we want to measure the risk in the multidimensional case without exploiting any scalarization technique of the random vector. We refer to the approach of the image space analysis in order to recall weak and strong Lagrangian duality results obtained through separation arguments. Finally, we interpret the shadow prices of the dual problem providing new definitions for risk aversion and non-satiability in the linear case.

Suggested Citation

  • Elisa Pagani, 2010. "Multiobjective Lagrangian duality for portfolio optimization with risk measures," Working Papers 18/2010, University of Verona, Department of Economics.
  • Handle: RePEc:ver:wpaper:18/2010

    Download full text from publisher

    File URL:
    File Function: First version
    Download Restriction: no

    More about this item


    Multivariate risk measures; Vector Optimization; Lagrangian Duality; Shadow prices; Image Space Analysis.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:ver:wpaper:18/2010. 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: (Michael Reiter). General contact details of provider: .

    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.