Abstract
In this paper, we present a filtering model on a default risk related to mathematical finance. We regard the first hitting time at zero of a one dimensional process which starts at some positive number and is not directly observed as the time when a default occurs. We discuss the conditional law of the hitting time under imperfect information. We use the reference measure change technique and some formula on a kind of conditional expectation to obtain a so-called hazard rate process. It is also discussed what the relation between the hazard rate process and the conditional law of the hitting time is like.
