Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty

TL;DR

This paper analyzes optimal consumption and investment decisions under Knightian uncertainty and market frictions, deriving explicit solutions and optimality conditions for complex intertemporal choices.

Contribution

It introduces a model incorporating local intertemporal substitution, nonlinear pricing, and explicit solutions in stationary markets, advancing understanding of decision-making under uncertainty.

Findings

Existence and uniqueness of optimal consumption plans proven.

Explicit solutions derived in stationary market settings.

Optimal consumption structure characterized via a backward equation.

Abstract

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.