Optimal control problems of Stochastic Volterra integral equations under Volatility Ambiguity

In this paper, we study the optimal control problems for stochastic Volterra integral equations driven by G-Brownian motion under Volatility Ambiguity.

With the help of G-stochastic analysis techniques and the weak convergence methods, we obtain the variation of the cost functional and the variational inequality.

Under the convexity assumptions, we establish the stochastic maximum principle, which serves as both a necessary and sufficient condition for optimal control.