Before revision:  The solution rests on the characterization of the value-function as the smallest stochastic super-solution that we establish .
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. 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) .