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.

Nonparametric statistical analysis of an upper bound of the ruin probability under large claims / Conti, Pier Luigi; Esterina, Masiello. - In: EXTREMES. - ISSN 1386-1999. - STAMPA. - 13:4(2010), pp. 439-461. [10.1007/s10687-009-0094-6]

Nonparametric statistical analysis of an upper bound of the ruin probability under large claims

CONTI, Pier Luigi;
2010

Abstract

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.
2010
insurance; ruin probability; asymptotics; poisson risk model; large claims; probability of ruin; nonparametric estimation; heavy-tailed distribution
01 Pubblicazione su rivista::01a Articolo in rivista
Nonparametric statistical analysis of an upper bound of the ruin probability under large claims / Conti, Pier Luigi; Esterina, Masiello. - In: EXTREMES. - ISSN 1386-1999. - STAMPA. - 13:4(2010), pp. 439-461. [10.1007/s10687-009-0094-6]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/362356
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