Credit Risk in an Economy with New Firms Arrivals

We propose a dynamic model to analyze the credit quality of firms. In the market in which they operate, the firms are divided into a finite number of classes representing their credit status. The cardinality of the population can increase, since new firms can enter in the market and the partition is supposed to change during the time, due to defaults and changes in credit quality, following a class of Markov processes. Several conditional probabilities related to default times are investigated and the role of occupation numbers in this context is highlighted. In a partial information setting in discrete time, we present a particle filtering technique to numerically compute by simulation the conditional distribution of the number of firms in the credit classes, given the information up to time t.