ON THE EVOLUTION AND ASYMPTOTIC ANALYSIS OF OPEN MARKOV POPULATIONS: APPLICATION TO CONSUMPTION CREDIT

In this paper, we study, by means of randomized sampling, the long-run stability of some open Markov population fed with time-dependent Poisson inputs. We show that state probabilities within transient states converge-even when the overall expected population dimension increases without bound-under general conditions on the transition matrix and input intensities. Following the convergence results, we obtain ML estimators for a particular sequence of input intensities, where the sequence of new arrivals is modeled by a sigmoidal function. These estimators allow for the forecast, by confidence intervals, of the evolution of the relative population structure in the transient states. Applying these results to the study of a consumption credit portfolio, we estimate the implicit default rate.