The object of this paper is the study of some asymptotic properties of the perturbed risk process with delayed claims, which is the sum of a Brownian motion with drift and a shot-noise whose underlying point process is a doubly stochastic Poisson process. More in particular, under suitable hypotheses, we show that it satisfies a large deviation principle, and we give asymptotic estimates of the corresponding ruin probabilities. Moreover, we introduce two suitable processes which can be seen as simplified versions of the original process, and we show some inequalities between the rate function and the Lundberg parameter concerning the original process, and the rate functions and the Lundberg parameters concerning the simplified versions, respectively.

Macci, C., Torrisi, G. (2004). Asymptotic results for perturbed risk processes with delayed claims. INSURANCE MATHEMATICS & ECONOMICS, 34, 307-320 [10.1016/j.insmatheco.2004.01.003].

Asymptotic results for perturbed risk processes with delayed claims

MACCI, CLAUDIO;
2004-01-01

Abstract

The object of this paper is the study of some asymptotic properties of the perturbed risk process with delayed claims, which is the sum of a Brownian motion with drift and a shot-noise whose underlying point process is a doubly stochastic Poisson process. More in particular, under suitable hypotheses, we show that it satisfies a large deviation principle, and we give asymptotic estimates of the corresponding ruin probabilities. Moreover, we introduce two suitable processes which can be seen as simplified versions of the original process, and we show some inequalities between the rate function and the Lundberg parameter concerning the original process, and the rate functions and the Lundberg parameters concerning the simplified versions, respectively.
2004
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Macci, C., Torrisi, G. (2004). Asymptotic results for perturbed risk processes with delayed claims. INSURANCE MATHEMATICS & ECONOMICS, 34, 307-320 [10.1016/j.insmatheco.2004.01.003].
Macci, C; Torrisi, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/31594
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