TY - JOUR A1 - Bouanani, Hafida A1 - Kebiri, Omar A1 - Hartmann, Carsten A1 - Redjil, Amel T1 - Optimal Relaxed Control for a Decoupled G-FBSDE JF - Journal of Optimization Theory and Applications N2 - AbstractIn 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. Y1 - 2024 U6 - https://doi.org/10.1007/s10957-024-02495-2 SN - 0022-3239 VL - 202 IS - 3 SP - 1027 EP - 1059 PB - Springer Science and Business Media LLC ER - TY - JOUR A1 - Boumezbeur, Zakaria A1 - Boutabia, Hacène A1 - Redjil, Amel A1 - Kebiri, Omar T1 - Differentiability of G-neutral stochastic differential equations with respect to parameter JF - Random Operators and Stochastic Equations N2 - In this paper, we study the differentiability of solutions of neutral stochastic differential equations driven by G-Brownian motion with respect to parameter. Under suitable assumptions, we show that solutions are differentiable with respect to the parameter which appears in the initial data. In addition, the stochastic differential equation of the derivative is given and the existence-uniqueness of solution is proved. Moreover, an example to illustrate the theoretically obtained results is presented. Y1 - 2024 U6 - https://doi.org//10.1515/rose-2024-2005 SN - 0926-6364 VL - 32 IS - 2 SP - 159 EP - 173 PB - Walter de Gruyter GmbH ER - TY - GEN A1 - Saci, Akram A1 - Redjil, Amel A1 - Boutabia, Hacene A1 - Kebiri, Omar T1 - Fractional stochastic differential equations driven by G-Brownian motion with delays T2 - Probability and Mathematical Statistics Y1 - 2023 U6 - https://doi.org/10.37190/0208-4147.00092 SN - 0208-4147 VL - 43 IS - 1 SP - 1 EP - 21 ER - TY - GEN A1 - Ben Gherbal, Hanane A1 - Redjil, Amel A1 - Kebiri, Omar T1 - The relaxed maximum principle for G-stochastic control systems with controlled jumps T2 - Advances in Mathematics: Scientific Journal Y1 - 2022 U6 - https://doi.org/10.37418/amsj.11.12.11 SN - 1857-8365 VL - 11 IS - 12 SP - 1313 EP - 1343 ER -