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The Fatou Closedness under Model Uncertainty

Author

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  • Marco Maggis
  • Thilo Meyer-Brandis
  • Gregor Svindland

Abstract

We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of $\mathcal{P}$-quasisure bounded random variables, where $\mathcal{P}$ is a (possibly non-dominated) class of probability measures. Applications of our results lie within robust versions the Fundamental Theorem of Asset Pricing or dual representation of convex risk measures.

Suggested Citation

  • Marco Maggis & Thilo Meyer-Brandis & Gregor Svindland, 2016. "The Fatou Closedness under Model Uncertainty," Papers 1610.04085, arXiv.org, revised Oct 2018.
    • Handle: RePEc:arx:papers:1610.04085
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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. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2015. "Model-free Superhedging Duality," Papers 1506.06608, arXiv.org, revised May 2016.
    3. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    4. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
    5. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    6. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    8. 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.
    9. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
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    Citations

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    Cited by:

    1. Felix-Benedikt Liebrich & Marco Maggis & Gregor Svindland, 2020. "Model Uncertainty: A Reverse Approach," Papers 2004.06636, arXiv.org, revised Mar 2022.
    2. Huy N. Chau & Masaaki Fukasawa & Miklos Rasonyi, 2021. "Super-replication with transaction costs under model uncertainty for continuous processes," Papers 2102.02298, arXiv.org.
    3. Johannes Langner & Gregor Svindland, 2022. "Bipolar Theorems for Sets of Non-negative Random Variables," Papers 2212.14259, arXiv.org, revised Feb 2024.
    4. Felix-Benedikt Liebrich & Max Nendel, 2020. "Separability vs. robustness of Orlicz spaces: financial and economic perspectives," Papers 2009.09007, arXiv.org, revised May 2021.
    5. Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
    6. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    7. Niushan Gao & Cosimo Munari, 2020. "Surplus-Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1342-1370, November.
    8. Huy N. Chau & Masaaki Fukasawa & Miklós Rásonyi, 2022. "Super‐replication with transaction costs under model uncertainty for continuous processes," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1066-1085, October.

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