On semiparametric estimation of ruin probabilities in the classical risk model

Esterina Masiello (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière

The ruin probability of an insurance company is a central topic in risk theory.We consider the classical Poisson risk model when the claim size distribution and the Poisson arrival rate are unknown. Given a sample of inter-arrival times and corresponding claims, we propose a semiparametric estimator of the ruin probability. We establish properties of strong consistency and asymptotic normality of the estimator and study bootstrap confidence bands. Further, we present a simulation example in order to investigate the finite sample properties of the proposed estimator.

Mots clés: asymptotics; Poisson risk model; ruin probability estimator; bootstrap; asymptotics.

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

Esterina Masiello. On semiparametric estimation of ruin probabilities in the classical risk model. Scandinavian Actuarial Journal, 2012, 2014 (4), pp.283-308. ⟨10.1080/03461238.2012.690247⟩. ⟨hal-00266449⟩