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Bellman type strategy for the continuous time mean-variance model

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  • Shuzhen Yang

Abstract

To investigate a time-consistent optimal strategy for the continuous time mean-variance model, we develop a new method to establish the Bellman principle. Based on this new method, we obtain a time-consistent dynamic optimal strategy that differs from the pre-committed and game-theoretic strategies. A comparison with the existing results on the continuous time mean-variance model shows that our method has several advantages. The explicit solutions of the dynamic optimal strategy and optimal wealth are given. When the dynamic optimal strategy is given at the initial time, we do not change it in the following investment time interval.

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  • Shuzhen Yang, 2020. "Bellman type strategy for the continuous time mean-variance model," Papers 2005.01904, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:2005.01904
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    References listed on IDEAS

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    1. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    2. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    3. Andrew E. B. Lim, 2004. "Quadratic Hedging and Mean-Variance Portfolio Selection with Random Parameters in an Incomplete Market," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 132-161, February.
    4. Bernard, C. & Vanduffel, S., 2014. "Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection," European Journal of Operational Research, Elsevier, vol. 234(2), pages 469-480.
    5. A. Bensoussan & K. Sung & S. Yam, 2013. "Linear–Quadratic Time-Inconsistent Mean Field Games," Dynamic Games and Applications, Springer, vol. 3(4), pages 537-552, December.
    6. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    7. Philip H. Dybvig, 1988. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 67-88.
    8. 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.
    9. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    10. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
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    Cited by:

    1. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
    2. Shen, Yang & Zou, Bin, 2021. "Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 68-80.
    3. Shuzhen Yang, 2020. "Discrete time multi-period mean-variance model: Bellman type strategy and Empirical analysis," Papers 2011.10966, arXiv.org.

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