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Document type:
Zeitschriftenaufsatz 
Author(s):
Pergamenshchikov, S. and Zeitouny, O. 
Title:
Ruin probability in the presence of risky investments 
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≤ Ψ(u) ≤ C*u 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. 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:
Pages contribution:
267-278 
Reviewed:
ja 
Language:
en 
Semester:
SS 06 
Format:
Text