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Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection

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  • Xiangyu Cui
  • Xun Li
  • Duan Li
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    Abstract

    The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posted a great challenge to our research community until recently. A few solution methods, including the embedding scheme, have been developed in the last decade to solve the dynamic mean-variance portfolio selection formulation successfully. We propose in this paper a novel mean-field framework that offers a more efficient modeling tool and a more accurate solution scheme in tackling directly the issue of nonseparability and deriving the optimal policies analytically for the multi-period mean-variance-type portfolio selection problems.

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    File URL: http://arxiv.org/pdf/1303.1064
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    Paper provided by arXiv.org in its series Papers with number 1303.1064.

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    Date of creation: Mar 2013
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    Handle: RePEc:arx:papers:1303.1064

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    Web page: http://arxiv.org/

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    1. Markus LEIPPOLD & Fabio TROJANI & Paolo VANINI, 2002. "A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities," FAME Research Paper Series, International Center for Financial Asset Management and Engineering rp48, International Center for Financial Asset Management and Engineering.
    2. Jianming Xia & Jia-An Yan, 2006. "Markowitz'S Portfolio Optimization In An Incomplete Market," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 16(1), pages 203-216.
    3. Ping Chen & Hailiang Yang, 2011. "Markowitz's Mean-Variance Asset-Liability Management with Regime Switching: A Multi-Period Model," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(1), pages 29-50.
    4. Celikyurt, U. & Ozekici, S., 2007. "Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach," European Journal of Operational Research, Elsevier, Elsevier, vol. 179(1), pages 186-202, May.
    5. Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(3), pages 387-406.
    6. Chiu, Mei Choi & Li, Duan, 2006. "Asset and liability management under a continuous-time mean-variance optimization framework," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 330-355, December.
    7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, American Finance Association, vol. 7(1), pages 77-91, 03.
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