work: the information-based approach and the reduced-form models. The first one has been developed in [@key-20] by Brody, Hughston and Macrina. They model the information concerning a random payoff $D_{T}$, paid at some pre-established date $T>0$, with the natural, completed filtration generated by the process $\xi=(\xi_{t},\,0\leq t\leq T)$, defined by $\xi_{t}:=\beta_{t}^{T}+\alpha tD_{T}$, where $\beta^{T}=(\beta_{t}^{T},\,0\leq t\leq T)$ is a standard Brownian bridge on the deterministic time interval $[0,T]$. The process $\beta^{T}$ is independent of $D_{T}$, and $\alpha>0$ is a positive constant. The idea is that the true information, represented by the component $\alpha tD_{T}$, about the final payoff is disturbed by some noisy information (rumors, mispricing, etc.), represented by the bridge process. In this model for credit risk the information concerning the random cash-flow $D_{T}$ is modeled explicitly but the default time $\tau$ of the company is not. On the other hand, in the models following the reduced-form approach for credit risk the information on the default time is modeled by the natural, completed filtration generated by the single-jump process $H=(H_{t}:=\mathbb{I}_{\{ \tau\leq t\} },\, t\geq0)$ occurring at $\tau$. We refer to the book [@key-21] of Bielecki and Rutkowski and the series of papers [@key-23; @key-24; @key-25] of Jeanblanc and Le Cam, 