Super-replication with proportional transaction cost under model uncertainty

TL;DR

This paper addresses super-replication in discrete-time financial markets with proportional transaction costs under model uncertainty, extending duality results through a novel randomization technique and minimax theorem.

Contribution

It introduces a new approach using randomization and minimax theorem to establish duality in super-replication with transaction costs under model uncertainty.

Findings

Established duality results in a non-dominated setting

Extended classical super-replication duality to uncertain models

Utilized a randomization technique to transform the problem

Abstract

We consider a discrete time financial market with proportional transaction cost under model uncertainty, and study a super-replication problem. We recover the duality results that are well known in the classical dominated context. Our key argument consists in using a randomization technique together with the minimax theorem to convert the initial problem to a frictionless problem set on an enlarged space. This allows us to appeal to the techniques and results of Bouchard and Nutz (2015) to obtain the duality result.