  In this work we consider a market with a term structure of credit risky bonds
in the single-name case. We aim at minimal assumptions extending existing
results in this direction. First, the random field of forward rates should be
driven by general semimartingales. We show that in this case, it is necessary
to extend the Heath-Jarrow-Morton approach to account for stochastic
discontinuities. We do so by introducing an additional component which is an
integral with respect to a random measure capturing those future jumps in the
term structure which are visible from the current time. Also the forward rates
for this second part are driven by general semimartingales. Finally, we pose
only minimal assumptions on the associated recovery scheme, i.e. the recovery
process is only assumed to be non-increasing.
  In this general setting we derive generalized drift conditions which
characterize when a given measure is a local martingale measure, thus yielding
no asymptotic free lunch with vanishing risk (NAFLVR), the right notion for
this large financial market to be free of arbitrage.
