Before revision:  An optimal consumption process, expressed in terms of the value function , is in a feedback form of the state process. The characterization of the value function relies on constructing a suitable sequence of approximating functions and employing viscosity solutions techniques. The derivation of the optimal consumption process involves a mixture of probabilistic arguments concerning the explosion and pathwise uniqueness of the controlled state process .
After revision:  An optimal consumption process, expressed in terms of the value function at the origin, which is the key to dealing with unbounded consumptions. Finally, relaxing the boundedness constraint is shown to increase, strictly, the expected utility at all wealth levels .