  We present a version of the fundamental theorem of asset pricing (FTAP) for
continuous time large financial markets with two filtrations in an
$L^p$-setting for $ 1 \leq p < \infty$. This extends the results of Yuri
Kabanov and Christophe Stricker \cite{KS:06} to continuous time and to a large
financial market setting, however, still preserving the simplicity of the
discrete time setting. On the other hand it generalizes Stricker's
$L^p$-version of FTAP \cite{S:90} towards a setting with two filtrations. We do
neither assume that price processes are semi-martigales, (and it does not
follow due to trading with respect to the \emph{smaller} filtration) nor that
price processes have any path properties, neither any other particular property
of the two filtrations in question, nor admissibility of portfolio wealth
processes, but we rather go for a completely general (and realistic) result,
where trading strategies are just predictable with respect to a smaller
filtration than the one generated by the price processes. Applications range
from modeling trading with delayed information, trading on different time
grids, dealing with inaccurate price information, and randomization approaches
to uncertainty.
