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No-arbitrage with multiple-priors in discrete time

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  • Blanchard, Romain
  • Carassus, Laurence

Abstract

In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. We show that it is equivalent to the existence of a subclass of priors having the same polar sets as the initial class and such that the uni-prior no-arbitrage holds true for all priors in this subset. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated.

Suggested Citation

  • Blanchard, Romain & Carassus, Laurence, 2020. "No-arbitrage with multiple-priors in discrete time," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6657-6688.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6657-6688
    DOI: 10.1016/j.spa.2020.06.006
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    References listed on IDEAS

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    1. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    2. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    4. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    5. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
    6. Laurence Carassus & Miklós Rásonyi, 2015. "On Optimal Investment For A Behavioral Investor In Multiperiod Incomplete Market Models," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 115-153, January.
    7. Marcel Nutz, 2016. "Utility Maximization Under Model Uncertainty In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 252-268, April.
    8. J. Jacod & A.N. Shiryaev, 1998. "Local martingales and the fundamental asset pricing theorems in the discrete-time case," Finance and Stochastics, Springer, vol. 2(3), pages 259-273.
    9. Beatrice Acciaio & Mathias Beiglbock & Friedrich Penkner & Walter Schachermayer, 2013. "A model-free version of the fundamental theorem of asset pricing and the super-replication theorem," Papers 1301.5568, arXiv.org, revised Mar 2013.
    10. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    11. repec:hal:wpaper:hal-01883787 is not listed on IDEAS
    12. Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
    13. Daniel Bartl, 2016. "Exponential utility maximization under model uncertainty for unbounded endowments," Papers 1610.00999, arXiv.org, revised Feb 2019.
    14. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    15. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    16. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem For Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 963-987, October.
    17. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    18. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Apr 2015.
    19. Erhan Bayraktar & Zhou Zhou, 2017. "On Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 988-1012, October.
    20. Mark H. A. Davis & David G. Hobson, 2007. "The Range Of Traded Option Prices," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 1-14, January.
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    2. Laurence Carassus, 2025. "Quasi-sure essential supremum and applications to finance," Finance and Stochastics, Springer, vol. 29(1), pages 219-260, January.
    3. Laurence Carassus, 2021. "Quasi-sure essential supremum and applications to finance," Papers 2107.12862, arXiv.org, revised Mar 2024.
    4. Dario Crisci & Sebastian E. Ferrando & Konrad Gajewski, 2025. "Agent-Based Models for Two Stocks with Superhedging," Papers 2503.18165, arXiv.org.
    5. Laurence Carassus & Johannes Wiesel, 2025. "Strategies with minimal norm are optimal for expected utility maximisation under high model ambiguity," Finance and Stochastics, Springer, vol. 29(2), pages 519-551, April.
    6. 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.
    7. Romain Blanchard & Laurence Carassus, 2021. "Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 366-398, January.

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