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Intertemporal Equilibria with Knightian uncertainty

Author

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  • Rose-Anne Dana

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

  • Franck Riedel

    (Center for mathematical economics - Universität Bielefeld)

Abstract

We study a dynamic and infinite-dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents' multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.

Suggested Citation

  • Rose-Anne Dana & Franck Riedel, 2013. "Intertemporal Equilibria with Knightian uncertainty," Post-Print hal-00927170, HAL.
  • Handle: RePEc:hal:journl:hal-00927170
    DOI: 10.1016/j.jet.2013.04.005
    Note: View the original document on HAL open archive server: https://hal.science/hal-00927170
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    Cited by:

    1. Antoine Billot & Sujoy Mukerji & Jean-Marc Tallon, 2020. "Market Allocations under Ambiguity: A Survey," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 267-282.
    2. Patrick Beissner & Frank Riedel, 2018. "Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty," Finance and Stochastics, Springer, vol. 22(3), pages 603-620, July.
    3. Patrick Beissner & Frank Riedel, 2014. "Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty," Papers 1409.6940, arXiv.org.
    4. Beißner, Patrick & Riedel, Frank, 2016. "Knight-Walras equilibria," Center for Mathematical Economics Working Papers 558, Center for Mathematical Economics, Bielefeld University.
    5. R.A Dana & C. Le Van, 2014. "Efficient allocations and Equilibria with short," Working Papers 2014-61, Department of Research, Ipag Business School.
    6. Jeleva, Meglena & Tallon, Jean-Marc, 2016. "Ambiguïté, comportements et marchés financiers," L'Actualité Economique, Société Canadienne de Science Economique, vol. 92(1-2), pages 351-383, Mars-Juin.
    7. repec:ipg:wpaper:2014-061 is not listed on IDEAS
    8. Patrick Beissner & Frank Riedel, 2019. "Equilibria Under Knightian Price Uncertainty," Econometrica, Econometric Society, vol. 87(1), pages 37-64, January.
    9. Eisei Ohtaki, 2023. "Optimality in an OLG model with nonsmooth preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 611-659, September.
    10. Gerasimou, Georgios, 2018. "On the indifference relation in Bewley preferences," Economics Letters, Elsevier, vol. 164(C), pages 24-26.
    11. Beißner, Patrick, 2016. "Radner Equilibria under Ambiguous Volatility," Center for Mathematical Economics Working Papers 493, Center for Mathematical Economics, Bielefeld University.
    12. Rose-Anne Dana & Cuong Le Van, 2014. "Efficient allocations and Equilibria with short-selling and Incomplete Preferences," Post-Print halshs-01020646, HAL.
    13. Giovanni Paolo Crespi & Andreas H. Hamel & Matteo Rocca & Carola Schrage, 2021. "Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 361-381, February.
    14. Eisei Ohtaki & Hiroyuki Ozaki, 2014. "Optimality in a Stochastic OLG Model with Ambiguity," Working Papers e069, Tokyo Center for Economic Research.
    15. repec:ipg:wpaper:201420 is not listed on IDEAS
    16. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
    17. Dana, R.A. & Le Van, C., 2014. "Efficient allocations and equilibria with short-selling and incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 101-105.
    18. Patrick Beissner, 2017. "Equilibrium prices and trade under ambiguous volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 213-238, August.
    19. Wei Ma, 2016. "Pareto Optimality and Indeterminacy of General Equilibrium under Knightian Uncertainty," Working Papers 201621, University of Pretoria, Department of Economics.
    20. Carlier, G. & Dana, R.-A., 2013. "Pareto optima and equilibria when preferences are incompletely known," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1606-1623.
    21. Tim J. Boonen & Fangda Liu & Ruodu Wang, 2021. "Competitive equilibria in a comonotone market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1217-1255, November.
    22. Gerasimou, Georgios, 2018. "On the indifference relation in Bewley preferences," Economics Letters, Elsevier, vol. 164(C), pages 24-26.
    23. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
    24. Tian, Dejian & Tian, Weidong, 2014. "Optimal risk-sharing under mutually singular beliefs," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 41-49.
    25. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2020. "Model-free bounds for multi-asset options using option-implied information and their exact computation," Papers 2006.14288, arXiv.org, revised Jan 2022.

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    More about this item

    Keywords

    Dynamic general equilibrium; No trade; General equilibrium theory; Incomplete preferences; Ambiguity; Knightian uncertaintyagainst uncertainty at all. . Dynamic general equilibrium; Knightian uncertaintyagainst uncertainty at all. .;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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