Optimal Consumption for Recursive Preferences with Local Substitution under Risk

TL;DR

This paper develops a rigorous framework for recursive intertemporal preferences with local substitution, analyzes the optimal consumption problem, and characterizes the structure of optimal plans using advanced mathematical tools.

Contribution

It introduces an infinite-dimensional Kuhn-Tucker theorem and provides a detailed geometric Poisson analysis of optimal consumption under recursive preferences.

Findings

Existence and uniqueness of optimal consumption plans established.

Necessary and sufficient conditions for optimality derived.

Structural insights into consumption plans within a geometric framework obtained.

Abstract

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.