Unified Optimality Conditions for Stochastic Optimal Control in the Rough Path and It\^o Frameworks

Excerpt

arXiv:2609.38395v1 Announce Type: cross Abstract: Stochastic differential equations (SDEs) can be studied via It\^{o} calculus and rough path theory. For stochastic optimal control, these two frameworks give distinct Pontryagin Maximum Principle (PMP) optimality conditions with forward-backward SDEs (FBSDEs) or rough differential equations. We show that the adjoint equations of the It\^{o} and rough PMPs are connected via the conditional expectation $p_t^{\text{It\^{o}}}=\mathbb{E}[p_t^{\text{ro