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

Emmanuel Lépinette and Amal Omrani ()
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Emmanuel Lépinette: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Amal Omrani: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Super-hedging problem Proportional transaction costs AIP condition Distorted Legendre-Fenchel transform Dynamic programming principle; Super-hedging problem; Proportional transaction costs; AIP condition; Distorted Legendre-Fenchel transform; Dynamic programming principle (search for similar items in EconPapers)
Date: 2025-11-04
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