Estimating the parameters of a seasonal Markov-modulated Poisson process

Armelle Guillou (1) , Stéphane Loisel (2) , Gilles Stupfler (3)

1 IRMA - Institut de Recherche Mathématique Avancée
2 SAF - Laboratoire de Sciences Actuarielle et Financière
3 CERGAM - Centre d'Études et de Recherche en Gestion d'Aix-Marseille

We present a new model of counting processes in insurance. The process is a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a simulation study.

Domaines: Théorie [stat.TH]

Armelle Guillou, Stéphane Loisel, Gilles Stupfler. Estimating the parameters of a seasonal Markov-modulated Poisson process. 2014. ⟨hal-00965279v1⟩