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Explicit Recursive Construction of Super-Replication Prices under Proportional Transaction Costs

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  • Emmanuel Lepinette
  • Amal Omrani

Abstract

We propose a constructive framework for the super-hedging problem of a European contingent claim under proportional transaction costs in discrete time. Our main contribution is an explicit recursive scheme that computes both the super-hedging price and the corresponding optimal strategy without relying on martingale arguments. The method is based on convex duality and a distorted Legendre--Fenchel transform, ensuring both tractability and convexity of the value functions. A numerical implementation on real market data illustrates the practical relevance of the proposed approach.

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  • Emmanuel Lepinette & Amal Omrani, 2025. "Explicit Recursive Construction of Super-Replication Prices under Proportional Transaction Costs," Papers 2503.02419, arXiv.org, revised Nov 2025.
    • Handle: RePEc:arx:papers:2503.02419
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/4654 is not listed on IDEAS
    2. Meriam El Mansour & Emmanuel Lépinette, 2020. "Conditional Interior and Conditional Closure of Random Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 356-369, November.
    3. Thai Huu Nguyen & Serguei Pergamenshchikov, 2017. "Approximate Hedging Problem With Transaction Costs In Stochastic Volatility Markets," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 832-865, July.
    4. Emmanuel Denis, 2010. "Approximate Hedging of Contingent Claims under Transaction Costs for General Pay-offs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 491-518.
    5. Yuri M. Kabanov & (*), Mher M. Safarian, 1997. "On Leland's strategy of option pricing with transactions costs," Finance and Stochastics, Springer, vol. 1(3), pages 239-250.
    6. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
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