Abstract
Let B(t), t ≥ 0 be a standard Brownian motion. In this paper, we derive the asymptotics of the probability of Parisian ruin over an infinite time horizon for the following risk process (Formula presented.) 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. It turns out that the Parisian ruin probability decays exponentially as u tends to infinity and is a decreasing function of the force of interest for u large. Moreover, we obtain the approximations of Parisian ruin time.
| Original language | English |
|---|---|
| Pages (from-to) | 514-528 |
| Number of pages | 15 |
| Journal | Scandinavian Actuarial Journal |
| Volume | 2018 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 3 Jul 2018 |
| Externally published | Yes |
Keywords
- Brownian motion
- Parisian ruin
- ruin probability
- ruin time
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Bai, L. (2018). Asymptotics of Parisian ruin of Brownian motion risk model over an infinite-time horizon. Scandinavian Actuarial Journal, 2018(6), 514-528. https://doi.org/10.1080/03461238.2017.1391872