  We study a linear diffusion process after its last exit time from a certain
regular point. Rather than treating the process as newly born at the last exit
time, we view the whole path and separate the original process before and after
the last exit time. This enables us not only to identify the transition
semigroup, boundary behavior, entrance law, and reverse of the post-last exit
time process, but also to establish a financial model for estimating the
loss-given-default distribution of corporate debt (an all-time important open
problem).
