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

2017/02/20 by Long Bai, Bai, Long
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability and Risk Models #math.PR #msc:60G15

paper · pdf · doi:10.48550/arxiv.1702.06091

10 pages

arxiv created 2017/02/20 · arxiv updated 2017/02/21

Abstract

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 R_u^δ(t)=e^δt(u+c∫^t₀e^-δvd v-σ∫₀^te^-δvd B(v)), 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. Further, we show the asymptotics of the Parisian ruin time of this risk process.

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