We study multiple defaults where the global market information is modelled as
progressive enlargement of filtrations. We shall provide a general pricing
formula by establishing a relationship between the enlarged filtration and the
reference default-free filtration in the random measure framework. On each
default scenario, the formula can be interpreted as a Radon-Nikodym derivative
of random measures. The contagion risks are studied in the multi-defaults
setting where we consider the optimal investment problem in a contagion risk
model and show that the optimization can be effectuated in a recursive manner
with respect to the default-free filtration
