Unified Optimality Conditions for Stochastic Optimal Control in the Rough Path and It o Frameworks
The paper unifies Itô and rough path optimality conditions for stochastic optimal control problems using a conditional expectation bridge. It shows that the adjoint equations from both frameworks are connected by E[prough_t | F_t], providing a single principle. This links FBSDE-based Itô methods with pathwise rough path methods, offering a new foundation for solving complex control problems.