IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v202y2024i3d10.1007_s10957-024-02495-2.html
   My bibliography  Save this article

Optimal Relaxed Control for a Decoupled G-FBSDE

Author

Listed:
  • Hafida Bouanani

    (University of Saida Dr Moulay Tahar)

  • Omar Kebiri

    (The Free University of Berlin
    University of Cottbus)

  • Carsten Hartmann

    (University of Cottbus)

  • Amel Redjil

    (Badji-Mokhtar University)

Abstract

In this paper we study a system of decoupled forward-backward stochastic differential equations driven by a G-Brownian motion (G-FBSDEs) with non-degenerate diffusion. Our objective is to establish the existence of a relaxed optimal control for a non-smooth stochastic optimal control problem. The latter is given in terms of a decoupled G-FBSDE. The cost functional is the solution of the backward stochastic differential equation at the initial time. The key idea to establish existence of a relaxed optimal control is to replace the original control problem by a suitably regularised problem with mollified coefficients, prove the existence of a relaxed control, and then pass to the limit.

Suggested Citation

  • Hafida Bouanani & Omar Kebiri & Carsten Hartmann & Amel Redjil, 2024. "Optimal Relaxed Control for a Decoupled G-FBSDE," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1027-1059, September.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:3:d:10.1007_s10957-024-02495-2
    DOI: 10.1007/s10957-024-02495-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02495-2
    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/s10957-024-02495-2?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. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Backward stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 759-784.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Wang, Bingjun & Yuan, Mingxia, 2019. "Forward-backward stochastic differential equations driven by G-Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 39-47.
    4. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1170-1195.
    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. Hu, Ying & Tang, Shanjian & Wang, Falei, 2022. "Quadratic G-BSDEs with convex generators and unbounded terminal conditions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 363-390.
    2. Hanwu Li & Yongsheng Song, 2021. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2285-2314, December.
    3. Kim, Kon-Gun & Kim, Mun-Chol & Hwang, Ho-Jin, 2024. "Representation of solutions to quadratic 2BSDEs with unbounded terminal values," Statistics & Probability Letters, Elsevier, vol. 213(C).
    4. Hu, Mingshang & Ji, Shaolin, 2017. "Dynamic programming principle for stochastic recursive optimal control problem driven by a G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 107-134.
    5. Shengqiu Sun, 2022. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Coefficients in (y, z)," Journal of Theoretical Probability, Springer, vol. 35(1), pages 370-409, March.
    6. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
    7. Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
    8. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    9. Hanwu Li & Falei Wang, 2019. "Stochastic Optimal Control Problem with Obstacle Constraints in Sublinear Expectation Framework," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 422-439, November.
    10. Song, Yongsheng, 2019. "Properties of G-martingales with finite variation and the application to G-Sobolev spaces," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2066-2085.
    11. Hu, Mingshang & Wang, Falei & Zheng, Guoqiang, 2016. "Quasi-continuous random variables and processes under the G-expectation framework," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2367-2387.
    12. Falei Wang & Guoqiang Zheng, 2021. "Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators," Journal of Theoretical Probability, Springer, vol. 34(2), pages 660-681, June.
    13. Hu, Mingshang & Ji, Xiaojun & Liu, Guomin, 2021. "On the strong Markov property for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 417-453.
    14. Hu, Mingshang & Wang, Falei, 2021. "Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 139-171.
    15. Wang, Bingjun & Yuan, Mingxia, 2019. "Forward-backward stochastic differential equations driven by G-Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 39-47.
    16. Ibrahim Dakaou & Abdoulaye Soumana Hima, 2021. "Large Deviations for Backward Stochastic Differential Equations Driven by G-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 34(2), pages 499-521, June.
    17. Li, Hanwu & Peng, Shige, 2020. "Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6556-6579.
    18. Li, Hanwu, 2019. "Optimal stopping under $\textit{G}$-expectation," Center for Mathematical Economics Working Papers 606, Center for Mathematical Economics, Bielefeld University.
    19. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    20. Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.

    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:202:y:2024:i:3:d:10.1007_s10957-024-02495-2. 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.