Before revision:  In our model, the risk free short rate follows a generalized Hull-White model. The default event occurs in an expected or unexpected manner when the firm value reaches a certain lower threshold - the default barrier at predetermined discrete announcing dates or  at the first jump time of a Poisson process with given default intensity , respectively .
After revision:  In our model, the risk free short rate process and firm value process. We assume that the default event occurs in an expected or unexpected manner when the firm value reaches a certain lower threshold - the default barrier at predetermined discrete announcing dates or at the first jump time of a Poisson process with given default intensity , respectively .