Urn and jump processes for modeling dependence and rating transitions in the field of credit risk

After the introduction of the Basel II-III regulatory framework for banks. Credit risk has officially become one of the main concerns of risk managers and regulators. Credit risk is the risk of the loss which may arise from the change of credit, such as defaults, variations in the credit quality of counterparties, etc. We aim at proposing more realistic and effective models for credit risk modelling using specially conceived urn processes. In particular, we plan to tackle three main issues in credit risk management: recovery risk, default dependence, and credit deterioration. All models will be deeply studied from a theoretical probabilistic point of view, but also applied to actual data, in order to test their practical usefulness. Possibly a unifying approach will be developed.