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

Emmanuel Lepinette and Amal Omrani

Papers from arXiv.org

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.

Date: 2025-03, Revised 2025-11
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