Parisian ruin of the Brownian motion risk model with constant force of interest

Détails

ID Serval
serval:BIB_B19CA92FB6CF
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Parisian ruin of the Brownian motion risk model with constant force of interest
Périodique
Statistics & Probability Letters
Auteur(s)
Bai  L., Luo  L.
ISSN
0167-7152 (Print)
Statut éditorial
Publié
Date de publication
2017
Peer-reviewed
Oui
Volume
120
Pages
34-44
Langue
anglais
Résumé
Let B(t), t is an element of R be a standard Brownian motion. Define a risk process
R-u(delta)(t) = e(delta t) (u + c integral(t)(0) e(-delta s) dB(s)), t >= 0, (0.1)
where u >= 0 is the initial reserve, delta >= 0 is, the force of interest, c > 0 is the rate of premium and sigma > 0 is a volatility factor. In this contribution we obtain an approximation of the Parisian ruin probability
K-S(delta) (u, T-u) := P { inf(t is an element of[0,S]) sup(S is an element of[t,t+Tu]) R-u(delta) (s) < 0}, S >= 0,
as u -> infinity no where T-u is a bounded function. Further, we show that the Parisian ruin time of this risk process can be approximated by an exponential random variable. Our results are new even for the classical ruin probability and ruin time which correspond to T-u equivalent to 0 in the Parisian setting.
Mots-clé
Parisian ruin, Ruin probability, Ruin time, Brownian motion
Web of science
Création de la notice
25/09/2016 11:35
Dernière modification de la notice
21/08/2019 5:15
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