Stochastic Maximum Principle for Stochastic Recursive Optimal Control Problem Under Volatility Ambiguity

We study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by $G$-Brownian motion. Some of the economic and financial optimization problems with volatility ambiguity can be formulated as such problems. Unlike the classical variational approach, we establish the maximum principle by the linearization and weak convergence methods.