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In this paper, we study a stochastic recursive optimal control problem inwhich the objective functional is described by the solution of a backwardstochastic differential equation driven by G-Brownian motion. Under standardassumptions, we establish the dynamic programming principle and the relatedHamilton-Jacobi-Bellman (HJB) equation in the framework of G-expectation.Finally, we show that the value function is the viscosity solution of theobtained HJB equation.

A stochastic recursive optimal control problem under the G-expectation framework