IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v167y2015i3d10.1007_s10957-015-0762-4.html
   My bibliography  Save this article

On Mean-Field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Lévy Processes

Author

Listed:
  • Mokhtar Hafayed

    (Biskra University)

  • Syed Abbas

    (School of Basic Sciences, Indian Institute of Technology)

  • Abdelmadjid Abba

    (Biskra University)

Abstract

In this paper, we study the mean-field-type partial information stochastic optimal control problem, where the system is governed by a controlled stochastic differential equation, driven by the Teugels martingales associated with some Lévy processes and an independent Brownian motion. We derive necessary and sufficient conditions of the optimal control for these mean-field models in the form of a maximum principle. The control domain is assumed to be convex. As an application, the partial information linear quadratic control problem of the mean-field type is discussed.

Suggested Citation

  • Mokhtar Hafayed & Syed Abbas & Abdelmadjid Abba, 2015. "On Mean-Field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Lévy Processes," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1051-1069, December.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-015-0762-4
    DOI: 10.1007/s10957-015-0762-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0762-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-015-0762-4?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. Mokhtar Hafayed & Syed Abbas, 2014. "On Near-Optimal Mean-Field Stochastic Singular Controls: Necessary and Sufficient Conditions for Near-Optimality," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 778-808, March.
    2. Mitsui, Ken-ichi & Tabata, Yoshio, 2008. "A stochastic linear-quadratic problem with Lévy processes and its application to finance," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 120-152, January.
    3. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alain Bensoussan & Boualem Djehiche & Hamidou Tembine & Sheung Chi Phillip Yam, 2020. "Mean-Field-Type Games with Jump and Regime Switching," Dynamic Games and Applications, Springer, vol. 10(1), pages 19-57, March.

    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. Buckdahn, Rainer & Chen, Yajie & Li, Juan, 2021. "Partial derivative with respect to the measure and its application to general controlled mean-field systems," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 265-307.
    2. Qun Shi, 2021. "Generalized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-77, June.
    3. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    4. Li, Juan, 2018. "Mean-field forward and backward SDEs with jumps and associated nonlocal quasi-linear integral-PDEs," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3118-3180.
    5. Wei Zhang & Hui Min, 2023. "$$L^p$$ L p -Error Estimates for Numerical Schemes for Solving Certain Kinds of Mean-Field Backward Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 36(2), pages 762-778, June.
    6. 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.
    7. Vassili Kolokoltsov & Marianna Troeva & Wei Yang, 2014. "On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players," Dynamic Games and Applications, Springer, vol. 4(2), pages 208-230, June.
    8. Roxana Dumitrescu & Bernt Øksendal & Agnès Sulem, 2018. "Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 559-584, March.
    9. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    10. Alain Bensoussan & Boualem Djehiche & Hamidou Tembine & Sheung Chi Phillip Yam, 2020. "Mean-Field-Type Games with Jump and Regime Switching," Dynamic Games and Applications, Springer, vol. 10(1), pages 19-57, March.
    11. Liangquan Zhang & Qing Zhou, 2018. "Near-Optimal Control of Stochastic Recursive Systems Via Viscosity Solution," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 363-382, August.
    12. Hao, Tao & Wen, Jiaqiang & Xiong, Jie, 2022. "Solvability of a class of mean-field BSDEs with quadratic growth," Statistics & Probability Letters, Elsevier, vol. 191(C).
    13. Kamal Boukhetala & Jean-François Dupuy, 2019. "Modélisation Stochastique et Statistique Book of Proceedings," Post-Print hal-02593238, HAL.
    14. Li, Juan & Liang, Hao & Mi, Chao, 2023. "A stochastic maximum principle for partially observed general mean-field control problems with only weak solution," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 397-439.
    15. Douissi, Soukaina & Wen, Jiaqiang & Shi, Yufeng, 2019. "Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 282-298.
    16. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    17. Salah Eddine Choutri & Tembine Hamidou, 2018. "A Stochastic Maximum Principle for Markov Chains of Mean-Field Type," Games, MDPI, vol. 9(4), pages 1-21, October.
    18. Fu, Guanxing & Horst, Ulrich & Xia, Xiaonyu, 2022. "Portfolio Liquidation Games with Self-Exciting Order Flow," Rationality and Competition Discussion Paper Series 327, CRC TRR 190 Rationality and Competition.
    19. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    20. Boualem Djehiche & Minyi Huang, 2016. "A Characterization of Sub-game Perfect Equilibria for SDEs of Mean-Field Type," Dynamic Games and Applications, Springer, vol. 6(1), pages 55-81, March.

    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:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-015-0762-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.