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 -