In this paper, we build a bridge between different reduced-form approaches to pricing defaultable claims. In particular, we showhow the well known formulas by Duffie et al. [12] and by Elliott et al.[14] are related. Moreover, in the spirit of Collin Dufresne et al. [8], wepropose a simple...

Filtrations have been introduced by Doob and have been a fundamentalfeature of the theory of stochastic processes. Most basic objects, such asmartingales, semimartingales, stopping times or Markov processes involvethe notion of filtration.[...]

In this paper, we provide a solution to two problems which have been open in default time modeling in credit risk. We first show that if $\tau$ is an arbitrary random (default) time such that its Az\'ema's supermartingale $Z_t^\tau=\P(\taut|\F_t)$ is continuous, then $\tau$ avoids stopping...