IDEAS home Printed from https://ideas.repec.org/a/taf/tsysxx/v47y2016i9p2078-2087.html
   My bibliography  Save this article

Exact optimal solution for a class of dual control problems

Author

Listed:
  • Suping Cao
  • Fucai Qian
  • Xiaomei Wang

Abstract

This paper considers a discrete-time stochastic optimal control problem for which only measurement equation is partially observed with unknown constant parameters taking value in a finite set of stochastic systems. Because of the fact that the cost-to-go function at each stage contains variance and the non-separability of the variance is so complicated that the dynamic programming cannot be successfully applied, the optimal solution has not been found. In this paper, a new approach to the optimal solution is proposed by embedding the original non-separable problem into a separable auxiliary problem. The theoretical condition on which the optimal solution of the original problem can be attained from a set of solutions of the auxiliary problem is established. In addition, the optimality of the interchanging algorithm is proved and the analytical solution of the optimal control is also obtained. The performance of this controller is illustrated with a simple example.

Suggested Citation

  • Suping Cao & Fucai Qian & Xiaomei Wang, 2016. "Exact optimal solution for a class of dual control problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(9), pages 2078-2087, July.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:9:p:2078-2087
    DOI: 10.1080/00207721.2014.973469
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207721.2014.973469
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207721.2014.973469?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Fucai Qian & Guo Xie & Ding Liu & Wenfang Xie, 2011. "Optimal control of LQG problem with an explicit trade-off between mean and variance," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(12), pages 1957-1964.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiang Meng, 2019. "Dynamic Mean-Variance Portfolio Optimisation," Papers 1907.03093, arXiv.org.
    2. Zhou Fang, 2023. "Continuous-Time Path-Dependent Exploratory Mean-Variance Portfolio Construction," Papers 2303.02298, arXiv.org.
    3. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    4. Xiangyu Cui & Xun Li & Duan Li & Yun Shi, 2014. "Time Consistent Behavior Portfolio Policy for Dynamic Mean-Variance Formulation," Papers 1408.6070, arXiv.org, revised Aug 2015.
    5. Zhang, Xili & Zhang, Weiguo & Xiao, Weilin, 2013. "Multi-period portfolio optimization under possibility measures," Economic Modelling, Elsevier, vol. 35(C), pages 401-408.
    6. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    7. Briec, Walter & Kerstens, Kristiaan, 2009. "Multi-horizon Markowitz portfolio performance appraisals: A general approach," Omega, Elsevier, vol. 37(1), pages 50-62, February.
    8. Xin Huang & Duan Li & Daniel Zhuoyu Long, 2020. "Scenario-decomposition Solution Framework for Nonseparable Stochastic Control Problems," Papers 2010.08985, arXiv.org.
    9. Shihao Zhu & Jingtao Shi, 2019. "Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full Information," Papers 1906.08410, arXiv.org, revised Jun 2020.
    10. Bekker, Paul A., 2004. "A mean-variance frontier in discrete and continuous time," CCSO Working Papers 200406, University of Groningen, CCSO Centre for Economic Research.
    11. Zhang, Miao & Chen, Ping, 2016. "Mean–variance asset–liability management under constant elasticity of variance process," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 11-18.
    12. Liu, Yong-Jun & Zhang, Wei-Guo, 2015. "A multi-period fuzzy portfolio optimization model with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 242(3), pages 933-941.
    13. Zhang, Caibin & Liang, Zhibin, 2022. "Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    14. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
    15. Shaolin Ji & Xiaomin Shi, 2016. "Explicit solutions for continuous time mean-variance portfolio selection with nonlinear wealth equations," Papers 1606.05488, arXiv.org.
    16. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
    17. Alessandra Milazzo & Elena Vigna, 2018. "The Italian Pension Gap: a Stochastic Optimal Control Approach," Carlo Alberto Notebooks 553, Collegio Carlo Alberto.
    18. Jun Yu, 2014. "Optimal Asset-Liability Management for an Insurer Under Markov Regime Switching Jump-Diffusion Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 317-330, November.
    19. In, Francis & Kim, Sangbae & Gençay, Ramazan, 2011. "Investment horizon effect on asset allocation between value and growth strategies," Economic Modelling, Elsevier, vol. 28(4), pages 1489-1497, July.
    20. Man Yiu Tsang & Tony Sit & Hoi Ying Wong, 2022. "Adaptive Robust Online Portfolio Selection," Papers 2206.01064, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:tsysxx:v:47:y:2016:i:9:p:2078-2087. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TSYS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.