Superreplication with proportional transaction cost under model uncertainty

Bruno Bouchard, Shuoqing Deng and Xiaolu Tan

Mathematical Finance, 2019, vol. 29, issue 3, 837-860

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.

Date: 2019
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