Ruin probability in the presence of risky investments

Sergey Pergamenshchikov () and Omar Zeitouny

Stochastic Processes and their Applications, 2006, vol. 116, issue 2, 267-278

Abstract: We consider an insurance company in the case when the premium rate is a bounded non-negative 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 [sigma]>0. If [beta]:=2a/[sigma]2-1>0 we find exact the asymptotic upper and lower bounds for the ruin probability [Psi](u) as the initial endowment u tends to infinity, i.e. we show that C*u-[beta][less-than-or-equals, slant][Psi](u)[less-than-or-equals, slant]C*u-[beta] for sufficiently large u. Moreover if ct=c*e[gamma]t with [gamma][less-than-or-equals, slant]0 we find the exact asymptotics of the ruin probability, namely [Psi](u)~u-[beta]. If [beta][less-than-or-equals, slant]0, we show that [Psi](u)=1 for any u[greater-or-equal, slanted]0.

Keywords: Risk; process; Geometric; Brownian; motion; Ruin; probability (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (7)

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