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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.


MSC classification: 93E20, 91B42, 60H30, 65C30