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

Long Bai*, Li Luo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Let B(t),t∈R be a standard Brownian motion. Define a risk process Ruδ(t)=eδt(u+c∫0te−δsds−σ∫0te−δsdB(s)),t≥0 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. In this contribution we obtain an approximation of the Parisian ruin probability KSδ(u,Tu):=P{inft∈[0,S]sups∈[t,t+Tu]Ruδ(s)<0},S≥0 as u→∞ where Tu 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 Tu≡0 in the Parisian setting.

Original languageEnglish
Pages (from-to)34-44
Number of pages11
JournalStatistics and Probability Letters
Publication statusPublished - 1 Jan 2017
Externally publishedYes


  • Brownian motion
  • Parisian ruin
  • Ruin probability
  • Ruin time


Dive into the research topics of 'Parisian ruin of the Brownian motion risk model with constant force of interest'. Together they form a unique fingerprint.

Cite this