Optimal Consumption for Recursive Preferences with Local Substitution under Risk

2024/09/12 by Hanwu Li, Li, Hanwu, Frank Riedel +1
Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2409.07799

openalex publication_date 2024/09/12 · openalex created_date 2024/10/23 · openalex updated_date 2026/07/28

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.

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