Optimal Control for a Zero-Sum Stochastic Differential Game with Noisy Memory Under G-Expectation

We study the optimal control for a zero-sum stochastic differential game with noisy memory under g-expectation where the dynamics is governed by a controlled Itô-Lévy process and the information available to the controller is possibly less than the overall information. Sufficient and necessary maximum principles for the optimal control of such systems are derived using Malliavin calculus techniques. As an illustration, we apply the result to a stochastic differential portfolio game problem in a financial model with memory and partial information.