  We analyse the structure of local martingale deflators projected on smaller
filtrations. In a general continuous-path setting, we show that the local
martingale part in the multiplicative Doob-Meyer decomposition of projected
local martingale deflators are themselves local martingale deflators in the
smaller information market. Via use of a Bayesian filtering approach, we
demonstrate the exact mechanism of how updates on the possible class of models
under less information result in the strict supermartingale property of
projections of such deflators. Finally, we demonstrate that these projections
are unable to span all possible local martingale deflators in the smaller
information market, by investigating a situation where market completeness is
not retained under filtration shrinkage.
