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Intertemporal Choice with Continuity Constraints

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  • Marcus Pivato

    (Théorie Economique, Modélisation et Applications (THEMA), CY Cergy Paris Université, 95000 Cergy, France)

Abstract

We consider a model of intertemporal choice where time is a continuum, the set of instantaneous outcomes (e.g., consumption bundles) is a topological space, and intertemporal plans (e.g., consumption streams) must be continuous functions of time. We assume that the agent can form preferences over plans defined on open time intervals. We axiomatically characterize the intertemporal preferences that admit a representation via discounted utility integrals. In this representation, the utility function is continuous and unique up to positive affine transformations, and the discount structure is represented by a unique Riemann–Stieltjes integral plus a unique linear functional measuring the long-run asymptotic utility.

Suggested Citation

  • Marcus Pivato, 2021. "Intertemporal Choice with Continuity Constraints," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1203-1229, August.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:3:p:1203-1229
    DOI: 10.1287/moor.2020.1091
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    1. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    2. Luc Lauwers, 2016. "Intergenerational Equity, Efficiency, and Constructibility," Studies in Economic Theory, in: Graciela Chichilnisky & Armon Rezai (ed.), The Economics of the Global Environment, pages 191-206, Springer.
    3. Daniel Kahneman & Peter P. Wakker & Rakesh Sarin, 1997. "Back to Bentham? Explorations of Experienced Utility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 375-406.
    4. J. A. Mirrlees, 1967. "Optimum Growth when Technology is Changing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 95-124.
    5. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    6. Graciela Chichilnisky, 1997. "What Is Sustainable Development?," Land Economics, University of Wisconsin Press, vol. 73(4), pages 467-491.
    7. Toyotaka Sakai, 2016. "Limit representations of intergenerational equity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 481-500, August.
    8. Arthur E. Attema & Han Bleichrodt & Kirsten I. M. Rohde & Peter P. Wakker, 2010. "Time-Tradeoff Sequences for Analyzing Discounting and Time Inconsistency," Management Science, INFORMS, vol. 56(11), pages 2015-2030, November.
    9. Hayashi, Takashi, 2003. "Quasi-stationary cardinal utility and present bias," Journal of Economic Theory, Elsevier, vol. 112(2), pages 343-352, October.
    10. Harvey, Charles M. & Østerdal, Lars Peter, 2012. "Discounting models for outcomes over continuous time," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 284-294.
    11. Peter Wakker, 1993. "Unbounded Utility for Savage's “Foundations of Statistics,” and Other Models," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 446-485, May.
    12. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    13. Marcus Pivato, 2020. "Subjective expected utility with a spectral state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 249-313, March.
    14. Hara, Kazuhiro, 2016. "Characterization of stationary preferences in a continuous time framework," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 34-43.
    15. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 231-257, April.
    16. José Luis Montiel Olea & Tomasz Strzalecki, 2014. "Axiomatization and Measurement of Quasi-Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1449-1499.
    17. Pivato, Marcus & Vergopoulos, Vassili, 2020. "Subjective expected utility with imperfect perception," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 104-122.
    18. , R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
    19. Lauwers, Luc, 2010. "Ordering infinite utility streams comes at the cost of a non-Ramsey set," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 32-37, January.
    20. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    21. Graciela Chichilnisky & Geoffrey Heal, 1997. "Social choice with infinite populations: construction of a rule and impossibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 303-318.
    22. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    23. Pan, Jinrui & Webb, Craig S. & Zank, Horst, 2015. "An extension of quasi-hyperbolic discounting to continuous time," Games and Economic Behavior, Elsevier, vol. 89(C), pages 43-55.
    24. Peter Fishburn & Ward Edwards, 1997. "Discount-neutral utility models for denumerable time streams," Theory and Decision, Springer, vol. 43(2), pages 139-166, September.
    25. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
    26. Wakker, Peter, 1993. "Additive representations on rank-ordered sets : II. The topological approach," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 1-26.
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    1. Lorenzo Bastianello & Vassili Vergopoulos, 2024. "Discounted Subjective Expected Utility in Continuous Time," Papers 2403.15319, arXiv.org.

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