Ruin probability in the presence of risky investments
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.
risk process, geometric Brownian motion, ruin probability