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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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