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Viability and arbitrage under Knightian Uncertainty

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  • Burzoni, Matteo

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

  • Soner, Halil Mete

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We reconsider the microeconomic foundations of financial economics under Knightian Uncertainty. In a general framework, we discuss the absence of arbitrage, its relation to economic viability, and the existence of suitable nonlinear pricing ex- pectations. Classical financial markets under risk and no ambiguity are contained as special cases, including various forms of the Efficient Market Hypothesis. For Knightian uncertainty, our approach unifies recent versions of the Fundamental Theorem of Asset Pricing under a common framework.

Suggested Citation

  • Burzoni, Matteo & Riedel, Frank & Soner, Halil Mete, 2017. "Viability and arbitrage under Knightian Uncertainty," Center for Mathematical Economics Working Papers 575, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:575
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Shuzhen Yang & Wenqing Zhang, 2024. "Asset pricing under model uncertainty with finite time and states," Papers 2408.13048, arXiv.org.
    3. Henry Chiu & Rama Cont, 2023. "A model‐free approach to continuous‐time finance," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 257-273, April.
    4. Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
    5. 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.
    6. Julian Holzermann, 2019. "Term Structure Modeling under Volatility Uncertainty," Papers 1904.02930, arXiv.org, revised Sep 2021.
    7. Tongseok Lim, 2023. "Replication of financial derivatives under extreme market models given marginals," Papers 2307.00807, arXiv.org.
    8. Gianluca Cassese, 2021. "Complete and competitive financial markets in a complex world," Finance and Stochastics, Springer, vol. 25(4), pages 659-688, October.
    9. Lorenzo Bastianello & Alain Chateauneuf & Bernard Cornet, 2022. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," Papers 2203.16292, arXiv.org.
    10. Julian Holzermann, 2018. "The Hull-White Model under Volatility Uncertainty," Papers 1808.03463, arXiv.org, revised Jan 2021.
    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. 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.
    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 & 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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).
    20. 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.

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    Keywords

    Robust Finance; No Arbitrage; Viability; Knightian Uncertainty;
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