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Superreplication with proportional transaction cost under model uncertainty

Author

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  • Bruno Bouchard
  • Shuoqing Deng
  • Xiaolu Tan

Abstract

We consider a discrete‐time financial market with proportional transaction cost under model uncertainty, and study a superreplication problem. We recover the duality results that are well known in the classical dominated context. Our key argument consists in using a randomization technique together with the minimax theorem to convert the initial problem to a frictionless problem on an enlarged space. This allows us to appeal to the techniques and results of Bouchard and Nutz to obtain the duality result.

Suggested Citation

  • Bruno Bouchard & Shuoqing Deng & Xiaolu Tan, 2019. "Superreplication with proportional transaction cost under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 837-860, July.
    • Handle: RePEc:bla:mathfi:v:29:y:2019:i:3:p:837-860
    DOI: 10.1111/mafi.12197
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    Citations

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    Cited by:

    1. Huy N. Chau & Masaaki Fukasawa & Miklos Rasonyi, 2021. "Super-replication with transaction costs under model uncertainty for continuous processes," Papers 2102.02298, arXiv.org.
    2. Bartl, Daniel, 2020. "Conditional nonlinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 785-805.
    3. Junbeom Lee & Xiang Yu & Chao Zhou, 2019. "Lifetime Ruin under High-watermark Fees and Drift Uncertainty," Papers 1909.01121, arXiv.org, revised Oct 2020.
    4. 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.
    5. Erhan Bayraktar & Matteo Burzoni, 2020. "On the quasi-sure superhedging duality with frictions," Finance and Stochastics, Springer, vol. 24(1), pages 249-275, January.
    6. Shuoqing Deng & Xiaolu Tan & Xiang Yu, 2020. "Utility Maximization with Proportional Transaction Costs Under Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1210-1236, November.
    7. Mun-Chol Kim & Song-Chol Ryom, 2022. "Pathwise superhedging under proportional transaction costs," Mathematics and Financial Economics, Springer, volume 16, number 4, March.
    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.
    9. 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.

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