  We discuss the pricing of defaultable assets in an incomplete information
model where the default time is given by a first hitting time of an
unobservable process. We show that in a fairly general Markov setting, the
indicator function of the default has an absolutely continuous compensator.
Given this compensator we then discuss the optional projection of a class of
semimartingales onto the filtration generated by the observation process and
the default indicator process. Available formulas for the pricing of
defaultable assets are analyzed in this setting and some alternative formulas
are suggested.
