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

2025/03/04 by Emmanuel Lépinette, Lepinette, Emmanuel, Amal Omrani +1
Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Risk and Portfolio Optimization #Financial Risk and Volatility Modeling

paper · doi:10.48550/arxiv.2503.02419

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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