Superreplication with Proportional Transaction Cost Under Model Uncertainty

Abstract

We consider a discrete‐time financial market with proportional transaction cost under model uncertainty, and study a superreplication 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 on an enlarged space. This allows us to appeal to the techniques and results of Bouchard and Nutz to obtain the duality result.

Keywords: duality, model uncertainty, superreplication, transaction cost