Default clustering in large portfolios: Typical events
  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. 
Kay Giesecke, Konstantinos Spiliopoulos, Richard B. Sowers
q-fin.RM math.PR q-fin.CP