Optimal consumption for recursive preferences with local substitution under risk

Hanwu Li and Frank Riedel

We explore intertemporal preferences that are recursive and account for local intertemporal substitution. First, we establish a rigorous foundation for these preferences and analyze their properties. Next, we examine the associated optimal consumption problem, proving the existence and uniqueness of the optimal consumption plan. We present an infinite-dimensional version of the Kuhn-Tucker theorem, which provides the necessary and sufficient conditions for optimality. Additionally, we investigate quantitative properties and the construction of the optimal consumption plan. Finally, we offer a detailed description of the structure of optimal consumption within a geometric Poisson framework.

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Year of publication:	[2024]
Authors:	Li, Hanwu ; Riedel, Frank
Publisher:	Bielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University
Subject:	recursive utility \| intertemporal substitution \| Hindy-Huang-Kreps preferences \| backward stochastic differential equation with jumps \| Poisson processes \| Stochastischer Prozess \| Stochastic process \| Intertemporale Entscheidung \| Intertemporal choice \| Präferenztheorie \| Theory of preferences \| Nutzenfunktion \| Utility function \| Nutzen \| Utility \| Konsumtheorie \| Consumption theory \| Analysis \| Mathematical analysis \| Nachfragetheorie des Haushalts \| Consumer demand theory \| Portfolio-Management \| Portfolio selection