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- W2964126064 abstract "Let B(t),t∈R be a standard Brownian motion. Define a risk process (0.1)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." @default.
- W2964126064 created "2019-07-30" @default.
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- W2964126064 date "2017-01-01" @default.
- W2964126064 modified "2023-09-26" @default.
- W2964126064 title "Parisian ruin of the Brownian motion risk model with constant force of interest" @default.
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- W2964126064 doi "https://doi.org/10.1016/j.spl.2016.09.011" @default.
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