  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.
