Discrete time approximation of fully nonlinear HJB equations via stochastic control problems under the $G$-expectation framework

In this paper, we propose a class of discrete-time approximation schemes for fully nonlinear Hamilton-Jacobi-Bellman (HJB) equations associated with stochastic optimal control problems under the $G$-expectation framework. We prove the convergence of the discrete schemes and determine the convergence rate. Several numerical examples are presented to illustrate the effectiveness of the obtained results.