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Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

Author

Listed:
  • Jaroslav Borovicka

    (New York University)

  • John Stachurski

    (Research School of Economics)

Abstract

We study existence, uniqueness and stability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences—one that analyzes principal eigenvalues of valuation operators and another that exploits the theory of monotone concave operators—we obtain conditions that are both necessary and sufficient for existence and uniqueness. We also show that the natural iterative algorithm is convergent if and only if a solution exists. Consumption processes are allowed to be nonstationary.

Suggested Citation

  • Jaroslav Borovicka & John Stachurski, 2018. "Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities," 2018 Meeting Papers 1275, Society for Economic Dynamics.
    • Handle: RePEc:red:sed018:1275
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    Cited by:

    1. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    2. Yu, Meng & Zhang, Junnan, 2019. "Equilibrium in production chains with multiple upstream partners," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 1-10.
    3. Drew D. Creal & Jing Cynthia Wu, 2020. "Bond risk premia in consumption‐based models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1461-1484, November.
    4. Gouin-Bonenfant, Emilien & Toda, Alexis Akira, 2018. "Pareto Extrapolation: Bridging Theoretical and Quantitative Models of Wealth Inequality," University of California at San Diego, Economics Working Paper Series qt90n2h2bb, Department of Economics, UC San Diego.
    5. Meng Yu & Junnan Zhang, 2019. "Equilibrium in Production Chains with Multiple Upstream Partners," Papers 1908.08208, arXiv.org.
    6. Borovička, Jaroslav & Stachurski, John, 2021. "Stability of equilibrium asset pricing models: A necessary and sufficient condition," Journal of Economic Theory, Elsevier, vol. 193(C).
    7. Flint O'Neil, 2020. "Existence and Uniqueness of Recursive Utility Models in $L_p$," Papers 2005.07067, arXiv.org.
    8. Thomas J. Sargent & John Stachurski, 2022. "Economic Networks: Theory and Computation," Papers 2203.11972, arXiv.org, revised Jul 2022.
    9. Massimo Marinacci & Luigi Montrucchio, 2019. "Unique Tarski Fixed Points," Management Science, INFORMS, vol. 44(4), pages 1174-1191, November.
    10. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    11. Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    12. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    13. Jing Guo & Xue Dong He, 2021. "Recursive Utility with Investment Gains and Losses: Existence, Uniqueness, and Convergence," Papers 2107.05163, arXiv.org.
    14. Christensen, Timothy M., 2022. "Existence and uniqueness of recursive utilities without boundedness," Journal of Economic Theory, Elsevier, vol. 200(C).
    15. Stachurski, John & Wilms, Ole & Zhang, Junnan, 2024. "Asset pricing with time preference shocks: Existence and uniqueness," Journal of Economic Theory, Elsevier, vol. 216(C).
    16. Qingyin Ma & John Stachurski & Alexis Akira Toda, 2018. "The Income Fluctuation Problem with Capital Income Risk: Optimality and Stability," Papers 1812.01320, arXiv.org.
    17. Fulop, Andras & Heng, Jeremy & Li, Junye & Liu, Hening, 2022. "Bayesian estimation of long-run risk models using sequential Monte Carlo," Journal of Econometrics, Elsevier, vol. 228(1), pages 62-84.
    18. Andras Fulop & Jeremy Heng & Junye Li, 2022. "Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models," Papers 2201.01094, arXiv.org.
    19. 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.
    20. Timothy M. Christensen, 2020. "Existence and uniqueness of recursive utilities without boundedness," Papers 2008.00963, arXiv.org, revised Aug 2021.

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    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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