Dynamic programming principle for stochastic optimal control problem under degenerate G-expectation

In this paper, we study a stochastic optimal control problem under degenerate G-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we prove that the value function is deterministic, and obtain the dynamic programming principle. Furthermore, we prove that the value function is the unique viscosity solution to the related HJB equation under degenerate case.
Comment: 17 pages