Before revision:  Building on the earlier work Larsen et al. ( 2014 ), we prove that the value of the problem is a Frechet-differentiable function of the drift of the price process, provided that this drift lies in a suitable Banach space.
After revision:  Building on the earlier work Larsen et al. ( 2016 ), we prove that the value of the problem is a Frechet-differentiable function of the drift of the price process, provided that this drift lies in a suitable Banach space.