Before revision:  The solution rests on the characterization of the value-function as (i) the unique stochastic solution of the associated HJB equation and as (ii) the pointwise smallest stochastic supersolution . We show that the optimal value process admits a dividend-penalty decomposition as sum of a martingale (associated to the penalty payment at ruin) and a potential (associated to the dividend payments). We find also an explicit necessary and sufficient condition  for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function.
After revision:  The solution rests on the characterization of the value-function as (i) the unique stochastic solution of the associated HJB equation and as (ii) the pointwise smallest stochastic supersolution of the associated HJB equation. Furthermore, a necessary and sufficient condition for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function.