Semi-static completeness and robust pricing by informed investors

TL;DR

This paper introduces the concept of semi-static completeness in continuous-time financial markets, characterizes its properties, and explores its implications for robust pricing with informed investors.

Contribution

It defines semi-static completeness, links it to extremality, and characterizes models where informed investors achieve semi-static completeness.

Findings

Semi-static completeness is equivalent to an extremality property.

Characterization of filtration structures for semi-static completeness.

Examples of robust pricing for informed and uninformed investors.

Abstract

We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework where a set of non-dominated models is given. The concept of semi-static completeness is introduced: it corresponds to having exact replication by means of semi-static strategies. We show that semi-static completeness is equivalent to an extremality property, and give a characterization of the induced filtration structure. Furthermore, we consider investors with additional information and, for specific types of extra information, we characterize the models that are semi-statically complete for the informed investors. Finally, we provide some examples where robust pricing for informed and uninformed agents can be done over semi-statically complete models.