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...

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the...

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.[...]

We build a general model for pricing defaultable claims. In addition to the usual ab-sence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when thedefault occurs. We prove that under this assumption, in some standard market ltrations, defaulttimes are...

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.[...]

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...