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- Title:
Ruin probability in the presence of risky investments
- Document type:
- Zeitschriftenaufsatz
- Author(s):
- Pergamenshchikov, S. and Zeitouny, O.
- Abstract:
- We consider an insurance company in the case when the premium rate is a bounded nonnegative random function ct and the capital of the insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a and volatility δ > 0. If β := 2a/δ² −1 > 0 we find exact the asymptotic upper and lower bounds for the ruin probability Ψ(u) as the initial endowment u tends to infinity, i.e. we show that C*u-β≤ Ψ(u) ≤ C*u-β for sufficiently large u. Moreover if ct= c*eΥt with Υ≤ 0 we find the exact asymptotics of the ruin probability, namely Ψ(u) ∼ u-β. If β ≤ 0, we show that Ψ(u) = 1 for any u ≥ 0.
- Keywords:
- risk process, geometric Brownian motion, ruin probability
- Journal title:
- Stoch. Proc. Appl.
- Year:
- 2006
- Journal volume:
- 116
- Journal issue:
- 2
- Pages contribution:
- 267-278
- Reviewed:
- ja
- Language:
- en
- Semester:
- SS 06
- Format:
- Text
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