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A polynomial optimization approach to constant rebalanced portfolio selection

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  • Yuichi Takano

    ()

  • Renata Sotirov

    ()

Abstract

We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on semidefinite programming. Our algorithm can solve problems that can not be handled by any of known polynomial optimization solvers. Copyright The Author(s) 2012

Suggested Citation

  • Yuichi Takano & Renata Sotirov, 2012. "A polynomial optimization approach to constant rebalanced portfolio selection," Computational Optimization and Applications, Springer, vol. 52(3), pages 645-666, July.
  • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:645-666
    DOI: 10.1007/s10589-011-9436-9
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    References listed on IDEAS

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    1. Maranas, C. D. & Androulakis, I. P. & Floudas, C. A. & Berger, A. J. & Mulvey, J. M., 1997. "Solving long-term financial planning problems via global optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1405-1425, June.
    2. Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095.
    3. Hibiki, Norio, 2006. "Multi-period stochastic optimization models for dynamic asset allocation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 365-390, February.
    4. Fleten, Stein-Erik & Hoyland, Kjetil & Wallace, Stein W., 2002. "The performance of stochastic dynamic and fixed mix portfolio models," European Journal of Operational Research, Elsevier, vol. 140(1), pages 37-49, July.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    7. Yuichi Takano & Jun-ya Gotoh, 2011. "Constant Rebalanced Portfolio Optimization Under Nonlinear Transaction Costs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(2), pages 191-211, May.
    8. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    More about this item

    Keywords

    Multi-period portfolio optimization; Polynomial optimization problem; Constant rebalancing; Semidefinite programming; Mean-variance criterion;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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