In this paper we give a financial justification, based on non arbitrage conditions,of the (H) hypothesis in default time modelling. We also show how the (H) hypothesis isaffected by an equivalent change of probability measure.[...]

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...