Information on a default time : Brownian bridges on a stochastic intervals and enlargement of filtrations.

Summary In this thesis work the information process regarding a default instant τ in a credit risk model is described by a Brownian bridge on the stochastic interval [0, τ]. Such a bridge process is characterized as more suitable in modeling than the classical model considering the indicator I[0, τ]. After studying the associated Bayes formulas, this approach to modeling default time information is linked with other financial market information. This is done using the theory of filtration magnification, where the filtration generated by the information process is expanded by the reference filtration describing other information not directly related with the default. Special attention is devoted to the classification of the defect time with respect to the minimum filtration but also to the expanded filtration. Sufficient conditions, under which τ is totally unreachable, are discussed, but also an example is given in which τ avoids downtime, is totally unreachable with respect to minimum filtration and predictable with respect to extended filtration. Finally, financial contracts such as, for example, private bonds and credit default swaps, are studied in the context described above.