To analyze the credit quality of a set of firms, a heterogeneous population of identical firms is studied inspired by models coming from the biological literature. The population is divided into a finite number of classes depending on the credit quality. The model is dynamic for different reasons. First, the cardinality of the population can increase since new firms can enter in the market. Then, due to changes in credit quality and to the defaults, a firm can move from a class to another. In a partial observing setting, under some markovianity assumptions, the problem of finding the conditional distribution of firms distance to defaults, given the observations, is discussed, using stochastic filtering techniques.
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