A dynamic version of the super-replication theorem under proportional transaction costs

TL;DR

This paper extends super-replication theorems to dynamic settings with proportional transaction costs, introducing generalized admissible strategies and establishing a well-defined, right-continuous super-replication price process.

Contribution

It provides a dynamic extension of super-replication theorems, including a generalized notion of admissible strategies and a well-defined super-replication price process.

Findings

Super-replication theorems are extended to dynamic settings.

A generalized notion of admissible strategies is introduced.

The super-replication price process is shown to be right-continuous.

Abstract

We extend the super-replication theorems of [27] in a dynamic setting, both in the num\'eraire-based as well as in the num\'eraire-free setting. For this purpose, we generalize the notion of admissible strategies. In particular, we obtain a well-defined super-replication price process, which is right-continuous under some regularity assumptions.