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Mean-variance portfolio selection with dynamic attention behavior in a hidden Markov model

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  • Y. Zhang
  • Z. Jin
  • J. Wei
  • G. Yin

Abstract

In this paper, we study closed-loop equilibrium strategies for mean-variance portfolio selection problem in a hidden Markov model with dynamic attention behavior. In addition to the investment strategy, the investor's attention to news is introduced as a control of the accuracy of the news signal process. The objective is to find equilibrium strategies by numerically solving an extended HJB equation by using Markov chain approximation method. An iterative algorithm is constructed and its convergence is established. Numerical examples are also provided to illustrate the results.

Suggested Citation

  • Y. Zhang & Z. Jin & J. Wei & G. Yin, 2022. "Mean-variance portfolio selection with dynamic attention behavior in a hidden Markov model," Papers 2205.08743, arXiv.org.
    • Handle: RePEc:arx:papers:2205.08743
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    References listed on IDEAS

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    1. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    2. Jin, Zhuo & Yin, G. & Wu, Fuke, 2013. "Optimal reinsurance strategies in regime-switching jump diffusion models: Stochastic differential game formulation and numerical methods," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 733-746.
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    5. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    6. Lixin Huang & Hong Liu, 2007. "Rational Inattention and Portfolio Selection," Journal of Finance, American Finance Association, vol. 62(4), pages 1999-2040, August.
    7. Antonio Gargano & Alberto G Rossi, 2018. "Does It Pay to Pay Attention?," The Review of Financial Studies, Society for Financial Studies, vol. 31(12), pages 4595-4649.
    8. Detemple, Jérôme B. & Kihlstrom, Richard E., 1987. "Acquisition d’information dans un modèle intertemporel en temps continu," L'Actualité Economique, Société Canadienne de Science Economique, vol. 63(2), pages 118-137, juin et s.
    9. Yihong Xia, 2001. "Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," Journal of Finance, American Finance Association, vol. 56(1), pages 205-246, February.
    10. Daniel Andrei & Michael Hasler, 2020. "Dynamic Attention Behavior Under Return Predictability," Management Science, INFORMS, vol. 66(7), pages 2906-2928, July.
    11. Zhuo Jin & G. Yin, 2013. "Numerical Methods for Optimal Dividend Payment and Investment Strategies of Markov-Modulated Jump Diffusion Models with Regular and Singular Controls," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 246-271, October.
    12. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    13. Elliott, Robert J. & Siu, Tak Kuen & Badescu, Alex, 2010. "On mean-variance portfolio selection under a hidden Markovian regime-switching model," Economic Modelling, Elsevier, vol. 27(3), pages 678-686, May.
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