  This paper considers general term structure models like the ones appearing in
portfolio credit risk modelling or life insurance. We give a general model
starting from families of forward rates driven by infinitely many Brownian
motions and an integer-valued random measure, generalizing existing approaches
in the literature. Then we derive drift conditions which are equivalent to no
asymptotic free lunch on the considered market. Existence results are also
given. In practice, models possessing a certain monotonicity are favorable and
we study general conditions which guarantee this. The setup is illustrated with
some examples.
