Optimal consumption with intertemporal substitution under knightian uncertainty

Giorgio Ferrari, Hanwu Li and Frank Riedel

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.

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Year of publication:	[2020]
Authors:	Ferrari, Giorgio ; Li, Hanwu ; Riedel, Frank
Publisher:	Bielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University
Subject:	Hindy-Huang-Kreps preferences \| Knightian uncertainty \| g-expectation \| ambiguityaversion \| singular stochastic control \| Entscheidung unter Unsicherheit \| Decision under uncertainty \| Konsumtheorie \| Consumption theory \| Risiko \| Risk \| Stochastischer Prozess \| Stochastic process \| Präferenztheorie \| Theory of preferences \| Intertemporale Entscheidung \| Intertemporal choice \| Nachfragetheorie des Haushalts \| Consumer demand theory \| Kontrolltheorie \| Control theory