@article{BouananiKebiriHartmannetal., author = {Bouanani, Hafida and Kebiri, Omar and Hartmann, Carsten and Redjil, Amel}, title = {Optimal Relaxed Control for a Decoupled G-FBSDE}, series = {Journal of Optimization Theory and Applications}, volume = {202}, journal = {Journal of Optimization Theory and Applications}, number = {3}, publisher = {Springer Science and Business Media LLC}, issn = {0022-3239}, doi = {10.1007/s10957-024-02495-2}, pages = {1027 -- 1059}, abstract = {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.}, language = {en} }