From the Decompositions of a Stopping Time to RiskPremium Decompositions

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 totally inaccessible stopping times; we therefore proceed to a systematic construction ofdefault times with particular emphasis on totally inaccessible stopping times.Surprisingly, this abstract mathematical construction, reveals a very specic and useful way inwhich default models can be built, using both market factors and idiosyncratic factors. We thenprovide all the relevant characteristics of a default time (i.e. the Azéma supermartingale and itsDoob-Meyer decomposition) given the information about these factors.[...]