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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.

Suggested Citation

  • 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:

    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. Shuzhen Yang & Wenqing Zhang, 2024. "Asset pricing under model uncertainty with discrete time and states," Papers 2408.13048, arXiv.org, revised Dec 2025.
    3. Cinfrignini, Andrea & Petturiti, Davide & Vantaggi, Barbara, 2023. "Dynamic bid–ask pricing under Dempster-Shafer uncertainty," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    4. Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2024. "Multi-agent equilibrium model with heterogeneous views on fundamental risks in incomplete market," CARF F-Series CARF-F-578, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2026.
    5. 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.
    6. Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
    7. Patrick Beissner, 2019. "Coherent-Price Systems and Uncertainty-Neutral Valuation," Risks, MDPI, vol. 7(3), pages 1-18, September.
    8. Staffa, Ruben Marek, 2023. "Macroeconomic effects from sovereign risk vs. Knightian uncertainty," IWH Discussion Papers 27/2023, Halle Institute for Economic Research (IWH).
    9. Michail Anthropelos & Paul Schneider, 2021. "Optimal Investment and Equilibrium Pricing under Ambiguity," Swiss Finance Institute Research Paper Series 21-78, Swiss Finance Institute.
    10. Nendel, Max & Streicher, Jan, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    11. 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.
    12. Ariel Neufeld & Matthew Ng Cheng En & Ying Zhang, 2024. "Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems," Papers 2403.09532, arXiv.org, revised Dec 2025.
    13. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    14. Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2024. "Multi-agent Equilibrium Model with Heterogeneous Views on Fundamental Risks in Incomplete Market," CIRJE F-Series CIRJE-F-1224, CIRJE, Faculty of Economics, University of Tokyo.
    15. 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.
    16. Emy Lécuyer & Victor Filipe Martins da Rocha, 2022. "Convex Asset Pricing," Working Papers hal-03916844, HAL.
    17. 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.
    18. Lécuyer, Emy & Riedel, Frank & Stanca, Lorenzo, 2024. "Arbitrage Pricing in Convex, Cash-Additive Markets," Center for Mathematical Economics Working Papers 694, Center for Mathematical Economics, Bielefeld University.
    19. Nendel, Max & Streicher, Jan, 2025. "An axiomatic approach to default risk and model uncertainty in rating systems," Center for Mathematical Economics Working Papers 725, Center for Mathematical Economics, Bielefeld University.
    20. Miftakhova, Alena, 2021. "Global sensitivity analysis for optimal climate policies: Finding what truly matters," Economic Modelling, Elsevier, vol. 105(C).
    21. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.

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