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

Author

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  • 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
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    Citations

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    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.
    2. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.

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