Portfolio optimization in a defaultable market under incomplete information

We consider the problem of maximization of expected utility from terminal wealth in a market model that is driven by a possibly not fully observable factor process and that takes explicitly into account the possibility of default for the individual assets as well as contagion (direct and information induced) among them. It is a multinomial model in discrete time that allows for an explicit solution. We discuss the solution within our defaultable and partial information setup, in particular we study its robustness. Numerical results are derived in the case of a log-utility function and they can be analogously obtained for a power utility function.