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

Paper: arXiv 2503.02419

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly novel and mathematically rigorous recursive framework using distorted Legendre-Fenchel transforms to solve discrete-time super-hedging under transaction costs without martingale measures. However, empirical rigor is low as it relies primarily on theoretical proofs with minimal details provided in the excerpt regarding empirical data validation.

Research Flowchart

  flowchart TD
    A[Goal: Explicit Super-Hedging Price & Strategy with Transaction Costs] --> B[Inputs: European Claim, Discrete Time Market Data & Transaction Costs]
    B --> C[Method: Convex Duality & Distorted Legendre-Fenchel Transform]
    C --> D[Process: Non-Martingale Explicit Recursive Construction Scheme]
    D --> E[Implementation: Numerical Validation on Real Market Data]
    E --> F[Outcomes: Convex Value Functions, Exact Super-Replication Price & Strategy]