TY - JOUR
T1 - Asymptotics of Parisian ruin of Brownian motion risk model over an infinite-time horizon
AU - Bai, Long
N1 - Publisher Copyright:
© 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/7/3
Y1 - 2018/7/3
N2 - Let B(t), t ≥ 0 be a standard Brownian motion. In this paper, we derive the asymptotics of the probability of Parisian ruin over an infinite time horizon for the following risk process (Formula presented.) where u ≥ 0 is the initial reserve, δ ≥ 0 is the force of interest, c > 0 is the rate of premium and σ > 0 is a volatility factor. It turns out that the Parisian ruin probability decays exponentially as u tends to infinity and is a decreasing function of the force of interest for u large. Moreover, we obtain the approximations of Parisian ruin time.
AB - Let B(t), t ≥ 0 be a standard Brownian motion. In this paper, we derive the asymptotics of the probability of Parisian ruin over an infinite time horizon for the following risk process (Formula presented.) where u ≥ 0 is the initial reserve, δ ≥ 0 is the force of interest, c > 0 is the rate of premium and σ > 0 is a volatility factor. It turns out that the Parisian ruin probability decays exponentially as u tends to infinity and is a decreasing function of the force of interest for u large. Moreover, we obtain the approximations of Parisian ruin time.
KW - Brownian motion
KW - Parisian ruin
KW - ruin probability
KW - ruin time
UR - http://www.scopus.com/inward/record.url?scp=85032207068&partnerID=8YFLogxK
U2 - 10.1080/03461238.2017.1391872
DO - 10.1080/03461238.2017.1391872
M3 - Article
AN - SCOPUS:85032207068
SN - 0346-1238
VL - 2018
SP - 514
EP - 528
JO - Scandinavian Actuarial Journal
JF - Scandinavian Actuarial Journal
IS - 6
ER -