@misc{RedjilGherbalKebiri, author = {Redjil, Amel and Gherbal, H. B. and Kebiri, Omar}, title = {Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps}, series = {Stochastic Analysis and Applications}, volume = {Vol. 41 (2023)}, journal = {Stochastic Analysis and Applications}, number = {1}, issn = {1532-9356}, doi = {10.1080/07362994.2021.1991809}, pages = {115 -- 133}, language = {en} } @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} } @article{BoumezbeurBoutabiaRedjiletal., author = {Boumezbeur, Zakaria and Boutabia, Hac{\`e}ne and Redjil, Amel and Kebiri, Omar}, title = {Differentiability of G-neutral stochastic differential equations with respect to parameter}, series = {Random Operators and Stochastic Equations}, volume = {32}, journal = {Random Operators and Stochastic Equations}, number = {2}, publisher = {Walter de Gruyter GmbH}, issn = {0926-6364}, doi = {/10.1515/rose-2024-2005}, pages = {159 -- 173}, abstract = {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.}, language = {en} } @misc{SaciRedjilBoutabiaetal., author = {Saci, Akram and Redjil, Amel and Boutabia, Hacene and Kebiri, Omar}, title = {Fractional stochastic differential equations driven by G-Brownian motion with delays}, series = {Probability and Mathematical Statistics}, volume = {43}, journal = {Probability and Mathematical Statistics}, number = {1}, issn = {0208-4147}, doi = {10.37190/0208-4147.00092}, pages = {1 -- 21}, language = {en} } @misc{BenGherbalRedjilKebiri, author = {Ben Gherbal, Hanane and Redjil, Amel and Kebiri, Omar}, title = {The relaxed maximum principle for G-stochastic control systems with controlled jumps}, series = {Advances in Mathematics: Scientific Journal}, volume = {11}, journal = {Advances in Mathematics: Scientific Journal}, number = {12}, issn = {1857-8365}, doi = {10.37418/amsj.11.12.11}, pages = {1313 -- 1343}, language = {en} }