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On recursive utilities with non-affine aggregator and conditional certainty equivalent

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  • Łukasz Balbus

    (University of Zielona Góra)

Abstract

In this paper, we consider the problem of the existence and the uniqueness of a recursive utility function defined on intertemporal lotteries. The purpose of this paper is to provide the results of the existence and the uniqueness of a recursive utility function. The utility function is obtained as the limit of iterations on a nonlinear operator and is independent on initial starting points, with iterations converging at an exponential rate. We also find the maximum utility and an optimal strategy by means of iterations of the Bellman operator.

Suggested Citation

  • Łukasz Balbus, 2020. "On recursive utilities with non-affine aggregator and conditional certainty equivalent," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 551-577, September.
    • Handle: RePEc:spr:joecth:v:70:y:2020:i:2:d:10.1007_s00199-019-01221-8
    DOI: 10.1007/s00199-019-01221-8
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    1. Le Van, Cuong & Vailakis, Yiannis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Journal of Economic Theory, Elsevier, vol. 123(2), pages 187-209, August.
    2. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2013. "A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1019-1039.
    3. Xiangyu Qu, 2017. "Separate aggregation of beliefs and values under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 503-519, February.
    4. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    5. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2012. "Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 115-132.
    6. Anna Jaśkiewicz & Janusz Matkowski & Andrzej Nowak, 2014. "On variable discounting in dynamic programming: applications to resource extraction and other economic models," Annals of Operations Research, Springer, vol. 220(1), pages 263-278, September.
    7. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2017. "On the sovereign debt paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(4), pages 825-846, December.
    8. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    9. Hansen, Lars-Peter & Sargent, Thomas-J, 2001. "Acknowledgement Misspecification in Macroeconomic Theory," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 19(S1), pages 213-227, February.
    10. Josef Haunschmied & Vladimir M. Veliov & Stefan Wrzaczek (ed.), 2014. "Dynamic Games in Economics," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-642-54248-0, July-Dece.
    11. Philippe Bich & Jean-Pierre Drugeon & Lisa Morhaim, 2018. "On temporal aggregators and dynamic programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 787-817, October.
    12. Bloise, Gaetano & Vailakis, Yiannis, 2018. "Convex dynamic programming with (bounded) recursive utility," Journal of Economic Theory, Elsevier, vol. 173(C), pages 118-141.
    13. Costis Skiadas, 2015. "Dynamic choice with constant source-dependent relative risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 393-422, November.
    14. Anderson, Evan W., 2005. "The dynamics of risk-sensitive allocations," Journal of Economic Theory, Elsevier, vol. 125(2), pages 93-150, December.
    15. Takao Asano & Hiroyuki Kojima, 2019. "Consequentialism and dynamic consistency in updating ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 223-250, July.
    16. John H. Boyd, 2006. "Discrete-Time Recursive Utility," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 9, pages 251-272, Springer.
    17. Geir B. Asheim & Tapan Mitra & Bertil Tungodden, 2016. "Sustainable Recursive Social Welfare Functions," Studies in Economic Theory, in: Graciela Chichilnisky & Armon Rezai (ed.), The Economics of the Global Environment, pages 165-190, Springer.
    18. Jean-Pierre Drugeon & Thai Ha-Huy & Thi Do Hanh Nguyen, 2019. "On maximin dynamic programming and the rate of discount," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 703-729, April.
    19. Ozaki, Hiroyuki & Streufert, Peter A., 1996. "Dynamic programming for non-additive stochastic objectives," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 391-442.
    20. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    21. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
    22. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    23. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2010. "Existence and Uniqueness of a Fixed Point for Local Contractions," Econometrica, Econometric Society, vol. 78(3), pages 1127-1141, May.
    24. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    25. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    26. Peter Klibanoff & Emre Ozdenoren, 2007. "Subjective recursive expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 49-87, January.
    27. Chew, Soo Hong & Epstein, Larry G, 1989. "The Structure of Preferences and Attitudes towards the Timing of the Resolution of Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(1), pages 103-117, February.
    28. Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), 2006. "Handbook on Optimal Growth 1," Springer Books, Springer, number 978-3-540-32310-5, November.
    29. Lars Peter Hansen & Thomas J. Sargent, 2001. "Acknowledging Misspecification in Macroeconomic Theory," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 519-535, July.
    30. Bäuerle, Nicole & Jaśkiewicz, Anna, 2018. "Stochastic optimal growth model with risk sensitive preferences," Journal of Economic Theory, Elsevier, vol. 173(C), pages 181-200.
    31. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    32. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
    33. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    34. Cuong Le Van & Yiannis Vailakis, 2005. "Recursive utility and optimal growth with bounded or unbounded returns," Post-Print halshs-00101201, HAL.
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    Cited by:

    1. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2022. "Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting," Journal of Economic Theory, Elsevier, vol. 204(C).
    2. Christensen, Timothy M., 2022. "Existence and uniqueness of recursive utilities without boundedness," Journal of Economic Theory, Elsevier, vol. 200(C).
    3. Anastasia Burkovskaya, 2022. "A model of state aggregation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 121-149, February.
    4. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.

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    More about this item

    Keywords

    Recursive utilities; Dynamic programming; Epstein–Zin preferences; Certainty equivalent; Solid cone; Attracting property;
    All these keywords.

    JEL classification:

    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers

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