Backward stochastic differential equations with Young drift

We show the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite q-variation with q∈[1,2).In contrast to previous work,we apply a direct fixpoint argument and do not rely on any type of flow decomposition.The resulting object is an effective tool to study semilinear rough partial differential equations via a Feynman–Kac type representation.