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Optimal Consumption for Recursive Preferences with Local Substitution under Risk

Author

Listed:
  • Li, Hanwu

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

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.

Suggested Citation

  • Li, Hanwu & Riedel, Frank, 2024. "Optimal Consumption for Recursive Preferences with Local Substitution under Risk," Center for Mathematical Economics Working Papers 693, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:693
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    File URL: https://pub.uni-bielefeld.de/download/2992835/2992836
    File Function: First Version, 2024
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    Keywords

    recursive utility; intertemporal substitution; Hindy-Huang-Kreps preferences; backward stochastic differential equation with jumps; Poisson processes;
    All these keywords.

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