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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

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    References listed on IDEAS

    1. Berger, Allen N. & DeYoung, Robert, 1997. "Problem loans and cost efficiency in commercial banks," Journal of Banking & Finance, Elsevier, vol. 21(6), pages 849-870, June.
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    4. Ricardo Brogi & Paolo Santella, 2004. "Two New Measures of Bankruptcy Efficiency," Chapters in SUERF Studies, SUERF - The European Money and Finance Forum.
    5. Demirguc-Kunt, Asli & Levine, Ross, 1999. "Bank-based and market-based financial systems - cross-country comparisons," Policy Research Working Paper Series 2143, The World Bank.
    6. Altug, Sumru G. & Usman, Murat, 2004. "Spillover Effects, Bank Lending and Growth," CEPR Discussion Papers 4320, C.E.P.R. Discussion Papers.
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    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

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