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Existence and uniqueness of recursive utilities without boundedness

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  • Christensen, Timothy M.

Abstract

This paper derives primitive, easily verifiable sufficient conditions for existence and uniqueness of (stochastic) recursive utilities for several important classes of preferences. In order to accommodate models commonly used in practice, we allow both the state space and per-period utilities to be unbounded. For many of the models we study, existence and uniqueness is established under a single, primitive “thin tail” condition on the distribution of growth in per-period utilities. We present several applications to robust preferences, models of ambiguity aversion and learning about hidden states, and Epstein–Zin preferences.

Suggested Citation

  • Christensen, Timothy M., 2022. "Existence and uniqueness of recursive utilities without boundedness," Journal of Economic Theory, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:jetheo:v:200:y:2022:i:c:s0022053122000035
    DOI: 10.1016/j.jet.2022.105413
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    Cited by:

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    2. Bloise, G. & Van, C. Le & Vailakis, Y., 2024. "An approximation approach to dynamic programming with unbounded returns," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    3. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    4. Stachurski, John & Wilms, Ole & Zhang, Junnan, 2024. "Asset pricing with time preference shocks: Existence and uniqueness," Journal of Economic Theory, Elsevier, vol. 216(C).
    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.
    6. Gaetano Bloise & Cuong Le Van & Yiannis Vailakis, 2024. "Do not Blame Bellman: It Is Koopmans' Fault," Econometrica, Econometric Society, vol. 92(1), pages 111-140, January.

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    More about this item

    Keywords

    Stochastic recursive utility; Ambiguity; Model uncertainty; Existence; Uniqueness;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E7 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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