We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firm defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to all firms, and past defaults. We prove a law of large numbers for the default rate in the pool, which describes the “typical” behavior of defaults.
"Default clustering in large portfolios: Typical events." Ann. Appl. Probab. 23 (1) 348 - 385, February 2013. https://doi.org/10.1214/12-AAP845