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Minimization of a Function of a Quadratic Functional with Application to Optimal Portfolio Selection

Author

Listed:
  • Zinoviy Landsman

    (University of Haifa)

  • Udi Makov

    (University of Haifa)

Abstract

We present an explicit closed-form solution to the problem of minimizing the combination of linear functional and a function of quadratic functional, subject to a system of affine constraints. This is of interest for solving important problems in financial economics related to optimal portfolio selection. The new results essentially generalize previous results of the authors concerning optimal portfolio selection with translation invariant and positive homogeneous risk measures. The classical mean-variance model and the recently introduced and investigated tail mean-variance model are special cases of the problem discussed here.

Suggested Citation

  • Zinoviy Landsman & Udi Makov, 2016. "Minimization of a Function of a Quadratic Functional with Application to Optimal Portfolio Selection," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 308-322, July.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-015-0856-z
    DOI: 10.1007/s10957-015-0856-z
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    References listed on IDEAS

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    1. Z. Landsman & U. Makov, 2011. "Translation-invariant and positive-homogeneous risk measures and optimal portfolio management," The European Journal of Finance, Taylor & Francis Journals, vol. 17(4), pages 307-320.
    2. Furman, Edward & Landsman, Zinoviy, 2006. "Tail Variance Premium with Applications for Elliptical Portfolio of Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 433-462, November.
    3. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    4. Landsman, Zinoviy, 2010. "On the Tail Mean-Variance optimal portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 547-553, June.
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    Citations

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    Cited by:

    1. Zhijun Xu & Jing Zhou, 2023. "A simultaneous diagonalization based SOCP relaxation for portfolio optimization with an orthogonality constraint," Computational Optimization and Applications, Springer, vol. 85(1), pages 247-261, May.
    2. Nicole Bauerle & Tomer Shushi, 2019. "Risk Management with Tail Quasi-Linear Means," Papers 1902.06941, arXiv.org, revised Jan 2020.
    3. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2018. "A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution," Risks, MDPI, vol. 6(1), pages 1-15, March.
    4. Tahsin Deniz Akturk & c{C}au{g}{i}n Ararat, 2019. "Portfolio optimization with two coherent risk measures," Papers 1903.10454, arXiv.org, revised Jul 2020.
    5. Tahsin Deniz Aktürk & Çağın Ararat, 2020. "Portfolio optimization with two coherent risk measures," Journal of Global Optimization, Springer, vol. 78(3), pages 597-626, November.

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