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Superhedging under Proportional Transaction Costs in Continuous Time

Author

Listed:
  • Atiqah Almuzaini
  • c{C}au{g}{i}n Ararat
  • Jin Ma

Abstract

We revisit the well-studied superhedging problem under proportional transaction costs in continuous time using the recently developed tools of set-valued stochastic analysis. By relying on a simple Black-Scholes-type market model for mid-prices and using continuous trading schemes, we define a dynamic family of superhedging sets in continuous time and express them in terms of set-valued integrals. We show that these sets, defined as subsets of Lebesgue spaces at different times, form a dynamic set-valued risk measure with multi-portfolio time-consistency. Finally, we transfer the problem formulation to a path-space setting and introduce approximate versions of superhedging sets that will involve relaxing the superhedging inequality, the superhedging probability, and the solvency requirement for the superhedging strategy with a predetermined error level. In this more technical framework, we are able to relate the approximate superhedging sets at different times by means of a set-valued Bellman's principle, which we believe will pave the way for a set-valued differential structure that characterizes the superhedging sets.

Suggested Citation

  • Atiqah Almuzaini & c{C}au{g}{i}n Ararat & Jin Ma, 2025. "Superhedging under Proportional Transaction Costs in Continuous Time," Papers 2511.18169, arXiv.org.
    • Handle: RePEc:arx:papers:2511.18169
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/5455 is not listed on IDEAS
    2. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    3. Zachary Feinstein & Birgit Rudloff & Jianfeng Zhang, 2022. "Dynamic Set Values for Nonzero-Sum Games with Multiple Equilibriums," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 616-642, February.
    4. Luciano Campi & Walter Schachermayer, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Finance and Stochastics, Springer, vol. 10(4), pages 579-596, December.
    5. Zachary Feinstein & Birgit Rudloff, 2013. "Time consistency of dynamic risk measures in markets with transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 13(9), pages 1473-1489, September.
    6. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    7. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    8. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    9. Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, vol. 8(4), pages 531-552, November.
    10. Yuri M. Kabanov & Günter Last, 2002. "Hedging under Transaction Costs in Currency Markets: a Continuous‐Time Model," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 63-70, January.
    11. Zachary Feinstein & Birgit Rudloff, 2015. "Multi-portfolio time consistency for set-valued convex and coherent risk measures," Finance and Stochastics, Springer, vol. 19(1), pages 67-107, January.
    12. repec:dau:papers:123456789/353 is not listed on IDEAS
    13. Michał Kisielewicz, 2020. "Set-Valued Stochastic Integrals and Applications," Springer Optimization and Its Applications, Springer, number 978-3-030-40329-4, March.
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