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On the Evolution and Asymptotic Analysis of Open Markov Populations: Application to Consumption Credit |
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| Authors: | Manuel L Esquível José M Fernandes |
| Institution: | 1. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal;2. CMA/FCT/UNL, Universidade Nova de Lisboa, Caparica, Portugal;3. CMA/FCT/UNL, Universidade Nova de Lisboa, Caparica, Portugal;4. Departamento de Ciências e Tecnologia, Universidade de Cabo-Verde, Praia, Cape Verde |
| Abstract: | 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. |
| Keywords: | Consumption Credit Markov Chains Open Populations Parameter Inference |