  In Bai and Paulsen (SIAM J. Control optim. 48, 2010) the optimal dividend
problem under transaction costs was analyzed for a rather general class of
diffusion processes. It was divided into several subclasses, and for the
majority of subclasses the optimal policy is a simple barrier policy; whenever
the process hits an upper barrier $\bar{u}^*$, reduce it to $\bar{u}^*-\xi$
through a dividend payment. After transaction costs, the shareholder receives
$k\xi-K$.
  It was proved that a simple barrier strategy is not always optimal, and here
these more difficult cases are solved. The optimal solutions are rather
complicated, but interesting.
