We develop a finite horizon continuous time market model, where risk averse
investors maximize utility from terminal wealth by dynamically investing in a
risk-free money market account, a stock written on a default-free dividend
process, and a defaultable bond, whose prices are determined via equilibrium.
We analyze financial contagion arising endogenously between the stock and the
defaultable bond via the interplay between equilibrium behavior of investors,
risk preferences and cyclicality properties of the default intensity.
The classical reduced-form and filtration expansion framework in credit risk
is extended to the case of multiple, non-ordered defaults, assuming that
conditional densities of the default times exist. Intensities and pricing
formulas are derived, revealing how information driven default contagion arises
in these models. We then analyze the impact of ordering the default times
before expanding the filtration.
In this paper we study progressive ?ltration expansions with random times. We
show how semimartingale decompositions in the expanded ?ltration can be
obtained using a natural link between progressive and initial expansions. The
link is, on an intuitive level, that the two coincide after the random time. We
make this idea precise and use it to establish known and new results in the
case of expansion with a single random time. The methods are then extended to
the multiple time case, without any restrictions on the ordering of the
individual times.