Huyen Pham (Université Paris 6): Stochastic control under progressive enlargement of filtrations and applications to default ris

 We formulate and investigate a general stochastic control problem under a progressive enlargement of filtration. The global information is enlarged from a reference
filtration and the knowledge of multiple random times together with associated marks
when they occur. By working under a density hypothesis on the conditional joint
distribution of the random times and marks, we prove a natural and useful decomposition
of the original stochastic control problem under the global filtration into classical
stochastic control problems under the reference filtration, which are determined in a
backward induction. This general study is motivated by optimization problems arising
in default risk management, and we provide applications of our decomposition result
for the indifference pricing of defaultable claim, and the optimal investment under bilateral
counterparty risk. The solutions are expressed in terms of BSDEs involving only
brownian filtration, and remarkably without jump component coming a priori from the
default times.