Superreplication with proportional transaction cost under model uncertainty

Bouchard, Bruno; Deng, Shuoqing; Tan, Xiaolu

Bouchard, Bruno; Deng, Shuoqing; Tan, Xiaolu (2018), Superreplication with proportional transaction cost under model uncertainty, Mathematical Finance. 10.1111/mafi.12197

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01569832

Date

2018

Journal name

Mathematical Finance

Publisher

Wiley

Abstract (EN)

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.

Subjects / Keywords

model uncertainty; duality; transaction cost; Super-replication