  We characterise the value function of the optimal dividend problem with a
finite time horizon as the unique classical solution of a suitable
Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by
a Skorokhod reflection of the fund's value at a time-dependent optimal
boundary. Our results are obtained by establishing for the first time a new
connection between singular control problems with an absorbing boundary and
optimal stopping problems on a diffusion reflected at $0$ and created at a rate
proportional to its local time.
