Before revision: We show that the equivalence between certain problems of singular stochastic control (SSC)  and related questions of optimal stopping known for convex performance criteria (see, for example ,  Karatzas and Shreve  (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.
After revision: We show that the equivalence between certain problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping known for convex performance criteria (see, for example , Karatzas and Shreve (1984) ) continues to hold in a non convex problem provided a related discretionary stopping time is introduced.