A filtering model on default risk (Q2743901)

The author introduces a filtering model for default risk, which is an extension of a model introduced by \textit{S. Kusuoka} [in: Advances in mathematical economics. Vol. 1, 69-82 (1999; Zbl 0939.60023)]. There are three processes \(X\), \(Z\) and \(Y\) involved in this model. \(X\) is a one-dimensional process starting from some positive number, and this process is called the main system. \(Z\) and \(Y\) are \(n\)- and \(m\)-dimensional processes and they are called the subsystem and observation, respectively. The first hitting time of zero by the main system is regarded as the default time. The author discusses the conditional law of the default time under imperfect information and obtains a formula for the so-called hazard rate process.