We analyze the intertemporal utility maximization problem under
uncertainty for the preferences proposed by Hindy, Huang and Kreps. Existence
and uniqueness of optimal consumption plans are established under arbitrary
convex portfolio constraints, including both complete and incomplete markets.
For the complete market setting, we prove an infinite-dimensional version of
the Kuhn –Tucker theorem which implies necessary and sufficient
conditions for optimality. Using this characterization, we show that optimal
plans prescribe consuming just enough to keep the induced level of satisfaction
always above some stochastic lower bound. When uncertainty is generated by a
Lévy process and agents exhibit constant relative risk aversion, we
derive solutions in closed form. Depending on the structure of the underlying
stochastics, optimal consumption occurs at rates, in gulps, or in a singular
way.