Parisian ruin of Brownian motion risk model over an infinite-time horizon

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Let B(t), t∈ R be a standard Brownian motion. In this paper, we derive the exact asymptotics of the probability of Parisian ruin on infinite time horizon for the following risk process alignRudef Rᵤδ(t)=eδᵗ(u+c∫ᵗ₀e⁻δᵛd v-σ∫₀ᵗe⁻δᵛd B(v)), t≥0, align 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. Further, we show the asymptotics of the Parisian ruin time of this risk process.