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An algebraic approach to integer portfolio problems

Author

Listed:
  • Castro, F.
  • Gago, J.
  • Hartillo, I.
  • Puerto, J.
  • Ucha, J.M.

Abstract

Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model. We propose an algebraic approach to maximize the expected return under a given admissible level of risk measured by the covariance matrix. To reach an optimal portfolio it is an essential ingredient the computation of different test sets (via Gröbner basis) of linear subproblems that are used in a dual search strategy.

Suggested Citation

  • Castro, F. & Gago, J. & Hartillo, I. & Puerto, J. & Ucha, J.M., 2011. "An algebraic approach to integer portfolio problems," European Journal of Operational Research, Elsevier, vol. 210(3), pages 647-659, May.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:3:p:647-659
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    Cited by:

    1. Leal, Marina & Ponce, Diego & Puerto, Justo, 2020. "Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs," European Journal of Operational Research, Elsevier, vol. 284(2), pages 712-727.
    2. Blanco, Víctor, 2011. "A mathematical programming approach to the computation of the omega invariant of a numerical semigroup," European Journal of Operational Research, Elsevier, vol. 215(3), pages 539-550, December.
    3. Daniel Felix Ahelegbey & Paolo Giudici & Fatemeh Mojtahedi, 2022. "Crypto Asset Portfolio Selection," FinTech, MDPI, vol. 1(1), pages 1-9, February.
    4. González-Díaz, Julio & González-Rodríguez, Brais & Leal, Marina & Puerto, Justo, 2021. "Global optimization for bilevel portfolio design: Economic insights from the Dow Jones index," Omega, Elsevier, vol. 102(C).
    5. Löschenbrand, Markus, 2020. "Finding multiple Nash equilibria via machine learning-supported Gröbner bases," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1178-1189.
    6. Fereshteh Vaezi & Seyed Jafar Sadjadi & Ahmad Makui, 2019. "A portfolio selection model based on the knapsack problem under uncertainty," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-19, May.
    7. J. Gago-Vargas & I. Hartillo & J. Puerto & J. Ucha, 2015. "An improved test set approach to nonlinear integer problems with applications to engineering design," Computational Optimization and Applications, Springer, vol. 62(2), pages 565-588, November.

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