Optimal consumption with intolerance for declining standard of living under nonlinear expectations

In this paper, we study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which consumer’s preferences exhibit intolerance for declining consumption. We further incorporate market frictions through a nonlinear pricing operator. A set of sufficient first-order conditions for optimality is derived, and the uniqueness and time-consistency of the optimal consumption plan are established. By a backward equation, we characterize the structure of optimal consumption plans. Explicit solutions are obtained in a stationary setting with a financial market that features distinct risk premia for short and long positions. Finally, we analyze the relationship between consumption level and relevant parameters.