We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent's preferences exhibit local intertemporal substitution. We also allow for
market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions
for optimality. With the help of a backward equation, we are able to determine the structure
of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the
financial market has different risk premia for short and long positions.
