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Equilibria Under Knightian Price Uncertainty

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  • Beissner, Patrick

    (ANU)

  • Riedel, Frank

    (IMW Bielefeld University)

Abstract
We study economies in which agents face Knightian uncertainty about state prices. Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such equilibria lead to Pareto inefficient allocations; the equilibria coincide with Arrow-Debreu equilibria only if the values of net trades are ambiguity-free in the mean. In economies without aggregate uncertainty, inefficiencies are generic. We introduce a constrained efficiency concept, uncertainty-neutral efficiency, equilibrium allocations under price uncertainty are efficient in this constrained sense. Arrow-Debreu equilibria turn out to be non-robust with respect to the introduction of Knightian uncertainty.

Suggested Citation

  • Beissner, Patrick & Riedel, Frank, 2019. "Equilibria Under Knightian Price Uncertainty," Rationality and Competition Discussion Paper Series 142, CRC TRR 190 Rationality and Competition.
    • Handle: RePEc:rco:dpaper:142
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    Cited by:

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    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.
    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. Michail Anthropelos & Paul Schneider, 2021. "Optimal Investment and Equilibrium Pricing under Ambiguity," Swiss Finance Institute Research Paper Series 21-78, Swiss Finance Institute.
    8. Patrick Beissner, 2019. "Coherent-Price Systems and Uncertainty-Neutral Valuation," Risks, MDPI, vol. 7(3), pages 1-18, September.
    9. Staffa, Ruben Marek, 2023. "Macroeconomic effects from sovereign risk vs. Knightian uncertainty," IWH Discussion Papers 27/2023, Halle Institute for Economic Research (IWH).
    10. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
    11. 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).
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Emy Lécuyer & Victor Filipe Martins da Rocha, 2022. "Convex Asset Pricing," Working Papers hal-03916844, HAL.
    18. 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.
    19. Miftakhova, Alena, 2021. "Global sensitivity analysis for optimal climate policies: Finding what truly matters," Economic Modelling, Elsevier, vol. 105(C).

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