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

详细信息    查看全文

• 作者：Long Bai^a ; ^{long.bai@unil.ch" class="auth_mail" title="E-mail the corresponding author} ; Li Luo^a ; ^b ; ^{Li.Luo@unil.ch" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 60G15 ; secondary ; 60G70
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：120
• 期：Complete
• 页码：34-44
• 全文大小：424 K

文摘

Let 8bed6ad75aaa" title="Click to view the MathML source">B(t),t∈R$B\left(t\right),t\in \mathbb{R}$ be a standard Brownian motion. Define a risk process where 8b3a01" title="Click to view the MathML source">u≥0$u\ge 0$ is the initial reserve, aa87232aa2504" title="Click to view the MathML source">δ≥0$\delta \ge 0$ is the force of interest, 8bda9502e61ecb6a40b21e0f0391f" title="Click to view the MathML source">c>0$c>0$ is the rate of premium and σ>0$\sigma >0$ is a volatility factor. In this contribution we obtain an approximation of the Parisian ruin probability as u→∞$u\to \infty$ where 8b6e95e99902237dc" title="Click to view the MathML source">T_u$T_u$ 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 b4bed322a5d5503117b781a" title="Click to view the MathML source">T_u≡0$T_u\equiv 0$ in the Parisian setting.