Nonparametric statistical analysis of ruin probability under large claims

Pier Luigi Conti (1) , Esterina Masiello (1)

1 Dipartimento di Statistica, Probabilità e Statistiche Applicate

In this paper, the classical Poisson risk model is considered. The claims are supposed to be modeled by heavy-tailed distributions, so that the moment generating function does not exist. The attention is focused on the probability of ruin. We first provide a nonparametric estimator of an upper bound of the ruin probability by Willmot and Lin. Then, its asymptotic behavior is studied. Asymptotic confidence intervals are studied, as well as bootstrap confidence intervals. Results for possibly unstable models are also obtained.

Mots clés: heavy-tailed distribution; Poisson risk model; probability of ruin; nonparametric estimation; asymptotics; heavy-tailed distribution.

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

Pier Luigi Conti, Esterina Masiello. Nonparametric statistical analysis of ruin probability under large claims. Extremes, 2010, 13 (4), pp.439-461. ⟨10.1007/s10687-009-0094-6⟩. ⟨hal-01018874⟩