Modelling of Default Risk: Mathematicals Tools
March 30, 2000
Abstract: Our aim is to give a theoretical study for the modelling of default risk. We provide first a detailed analysis of the relatively simple case when the flow of information available to an agent reduces to the observations of the random time which models the default event. Subsequently, the case of the general filtration is examined. The focus is on the evaluation of conditional expectations with respect to the filtration generated by a default time with the use of the intensity function, and on various versions of the martingale representation theorem. For a more detailed account of the potential applications of results presented in this work in the context of the modelling of default risk, we refer to the companion work: M. Jeanblanc and M. Rutkowski: Modelling of Default Risk: An Overview.