Discrete-time risk models based on time series for count random variables.

Hélène Cossette (1) , Etienne Marceau (1) , Véronique Maume-Deschamps (2)

1 Ecole d'Actuariat
2 SAF - Laboratoire de Sciences Actuarielle et Financière

In this paper, we consider various spe...cations of the general discrete- time risk model in which a serial dependent structure is introduced between the claim numbers for each period. We consider risk models based on compound distributions assuming several examples of discrete variate time series as specific temporal dependence structures: Poisson MA(1) process, Poisson AR(1), Markov Bernoulli process and Markov switching regime process. In these models, we derive expressions for a function that allows us to find the Lundberg coeficient. Specific cases for which an explicit expression can be found for the Lundberg coe¢ cient are also presented. Numerical examples are provided to illustrate di¤erent topics discussed in the paper.

Mots clés: Discrete-time risk model; Poisson MA(1) process; Poisson AR(1) process; Lundberg Coe¢ cient; Lundberg Coe¢ cient.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [math.PR]

Hélène Cossette, Etienne Marceau, Véronique Maume-Deschamps. Discrete-time risk models based on time series for count random variables.. ASTIN Bulletin, 2010, 40 (1), pp.123-150. ⟨10.2143/AST.40.1.2049221⟩. ⟨hal-00504009⟩