  We consider the problem of modelling the term structure of defaultable bonds,
under minimal assumptions on the default time. In particular, we do not assume
the existence of a default intensity and we therefore allow for the possibility
of default at predictable times. It turns out that this requires the
introduction of an additional term in the forward rate approach by Heath,
Jarrow and Morton (1992). This term is driven by a random measure encoding
information about those times where default can happen with positive
probability. In this framework, we derive necessary and sufficient conditions
for a reference probability measure to be a local martingale measure for the
large financial market of credit risky bonds, also considering general recovery
schemes.
