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Equilibria Under Knightian Price Uncertainty

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  • Patrick Beissner
  • Frank Riedel

Abstract

We study economies with Knightian uncertainty about state prices. We introduce an equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such equilibria lead to inefficient allocations; they coincide with Arrow–Debreu equilibria if and only if the values of net trades are ambiguity‐free in mean. In economies without aggregate uncertainty, inefficiencies are generic. Equilibrium allocations under price uncertainty are efficient in a constrained sense that we call uncertainty–neutral efficient. Arrow–Debreu equilibria turn out to be non‐robust with respect to the introduction of Knightian uncertainty.

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  • Patrick Beissner & Frank Riedel, 2019. "Equilibria Under Knightian Price Uncertainty," Econometrica, Econometric Society, vol. 87(1), pages 37-64, January.
  • Handle: RePEc:wly:emetrp:v:87:y:2019:i:1:p:37-64
    DOI: 10.3982/ECTA14934
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    Cited by:

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    4. Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
    5. Michail Anthropelos & Paul Schneider, 2021. "Optimal Investment and Equilibrium Pricing under Ambiguity," Swiss Finance Institute Research Paper Series 21-78, Swiss Finance Institute.
    6. Patrick Beissner, 2019. "Coherent-Price Systems and Uncertainty-Neutral Valuation," Risks, MDPI, vol. 7(3), pages 1-18, September.
    7. Staffa, Ruben Marek, 2023. "Macroeconomic effects from sovereign risk vs. Knightian uncertainty," IWH Discussion Papers 27/2023, Halle Institute for Economic Research (IWH).
    8. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
    9. 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.
    10. Max Nendel & Jan Streicher, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Papers 2303.08217, arXiv.org, revised Sep 2023.
    11. Emy Lécuyer & Victor Filipe Martins da Rocha, 2022. "Convex Asset Pricing," Working Papers hal-03916844, HAL.
    12. 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.
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