The face-lifting theorem for proportional transaction costs in multiasset models

摘要

The paper presents a multi-dimensional version of the face-lifting theorem presented by Guasoni et al. [5] for the one-dimensional case. The theorem provides a closed-form solution to the superreplication problem of path-independent European options for proportional, infinitesimally small transaction costs in continuous time. This formula can be shown to hold true for all d-dimensional asset processes sharing a certain full-support property. Semimartingale or continuity assumptions made in earlier works could be dropped as well as certain restrictions on the payoff function. Examples concerning the impact of this result and sharpness of our assumptions are given.