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Dynamic programming with state-dependent discounting

Author

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  • Stachurski, John
  • Zhang, Junnan

Abstract

This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results can be recovered. We also show that the condition cannot be significantly weakened. Our framework is general enough to handle complications such as recursive preferences and unbounded rewards. Economic and financial applications are discussed.

Suggested Citation

  • Stachurski, John & Zhang, Junnan, 2021. "Dynamic programming with state-dependent discounting," Journal of Economic Theory, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jetheo:v:192:y:2021:i:c:s0022053121000077
    DOI: 10.1016/j.jet.2021.105190
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    Citations

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    Cited by:

    1. Cascaldi-Garcia, Danilo & Vukoti, Marija & Zubairy, Sarah, 2023. "Innovation During Challenging Times," The Warwick Economics Research Paper Series (TWERPS) 1475, University of Warwick, Department of Economics.
    2. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    3. Stachurski, John & Wilms, Ole & Zhang, Junnan, 2024. "Asset pricing with time preference shocks: Existence and uniqueness," Journal of Economic Theory, Elsevier, vol. 216(C).
    4. Alexis Akira Toda, 2021. "Perov's Contraction Principle and Dynamic Programming with Stochastic Discounting," Papers 2103.14173, arXiv.org, revised Sep 2021.
    5. Stachurski, John & Wilms, Ole & Zhang, Junnan, 2024. "Asset pricing with time preference shocks: Existence and uniqueness," Other publications TiSEM 29da00af-3cca-4717-aa55-a, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    Dynamic programming; Optimality; State-dependent discounting;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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