Credit risk modeling under incomplete information

In this work we study a class of credit default models with imperfect information. We combine the ideas of both structural and reduced form models, within a partial observation framework in which the information could even be delayed. Assuming that default is triggered by the touch-down of the firm total asset process to a prescribed and possibly random barrier, our main purpose is to obtain the default probability, as a continuous function of a hidden Markovian factor process, conditioning on the observed continuous and jump information. We show that a separation principle of nonlinear filtering is still valid in such a setting, and the default intensity can be estimated through the filtered factor process, which is the solution of a Riccati-type of Stochastic SDE driven by the underlying Brownian motion and counting process. Some Bayesian inference theory is also applied to obtain our solutions