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

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• 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 B(t),t∈R$B\left(t\right),t\in \mathbb{R}$ be a standard Brownian motion. Define a risk process where u≥0$u\ge 0$ is the initial reserve, δ≥0$\delta \ge 0$ is the force of interest, 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 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 T_u≡0$T_u\equiv 0$ in the Parisian setting.