F.: Optimal consumption choice under uncertainty with intertemporal substitution

We extend the analysis of the intertemporal utility maximization problem for Hindy-Huang-Kreps utilities reported in Bank and Riedel (1998) to the stochastic case. Existence and uniqueness of optimal consumption plans are established under arbitrary convex portfolio constraints, including both com-plete and incomplete markets. For the complete market setting, Kuhn-Tucker-like necessary and sucient conditions for optimality are given. Using this characterization, we show that optimal consumption plans are obtained by re-ecting the associated level of satisfaction on a stochastic lower bound. When uncertainty is generated by a LØvy process and agents exhibit constant relative risk aversion, closed-form solutions are derived. Depending on the structure of the underlying stochastics, optimal consumption occurs at rates, in gulps, or singular to Lebesgue measure