  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.
