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Viability and Arbitrage Under Knightian Uncertainty

Author

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  • Matteo Burzoni
  • Frank Riedel
  • H. Mete Soner
Abstract
We reconsider the microeconomic foundations of financial economics. Motivated by the importance of Knightian uncertainty in markets, we present a model that does not carry any probabilistic structure ex ante, yet is based on a common order. We derive the fundamental equivalence of economic viability of asset prices and absence of arbitrage. We also obtain a modified version of the fundamental theorem of asset pricing using the notion of sublinear pricing measures. Different versions of the efficient market hypothesis are related to the assumptions one is willing to impose on the common order.

Suggested Citation

  • Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:3:p:1207-1234
    DOI: 10.3982/ECTA16535
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    4. Hölzermann, Julian & Lin, Qian, 2019. "Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian Motion," Center for Mathematical Economics Working Papers 613, Center for Mathematical Economics, Bielefeld University.
    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. Lorenzo Bastianello & Alain Chateauneuf & Bernard Cornet, 2022. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," Papers 2203.16292, arXiv.org.
    8. Jan Obłój & Johannes Wiesel, 2021. "A unified framework for robust modelling of financial markets in discrete time," Finance and Stochastics, Springer, vol. 25(3), pages 427-468, July.
    9. Tongseok Lim, 2023. "Replication of financial derivatives under extreme market models given marginals," Papers 2307.00807, arXiv.org.
    10. Matteo Burzoni & Mario Sikic, 2018. "Robust martingale selection problem and its connections to the no-arbitrage theory," Papers 1801.03574, arXiv.org, revised Nov 2018.
    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. Tolulope Fadina & Thorsten Schmidt, 2019. "Default Ambiguity," Risks, MDPI, vol. 7(2), pages 1-17, June.
    14. Luca Galimberti & Anastasis Kratsios & Giulia Livieri, 2022. "Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis," Papers 2210.13300, arXiv.org, revised May 2023.
    15. 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.
    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. Hölzermann, Julian, 2018. "Bond Pricing under Knightian Uncertainty. A Short Rate Model with Drift and Volatility Uncertainty," Center for Mathematical Economics Working Papers 582, Center for Mathematical Economics, Bielefeld University.
    18. Julian Holzermann, 2019. "Term Structure Modeling under Volatility Uncertainty," Papers 1904.02930, arXiv.org, revised Sep 2021.
    19. Henry Chiu & Rama Cont, 2023. "A model‐free approach to continuous‐time finance," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 257-273, April.
    20. 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.

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