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# Ruin probability in the presence of risky investments

## Author

Listed:
• Serguei Pergamenchtchikov

(LMRS)

• Zeitouny Omar

(LMRS)

## Abstract

We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ 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 $C_*u^{-\beta}\le\Psi(u)\le C^*u^{-\beta}$ for sufficiently large $u$. Moreover if $c_\zs{t}=c^*e^{\gamma t}$ with $\gamma\le 0$ we find the exact asymptotics of the ruin probability, namely $\Psi(u)\sim u^{-\beta}$. If $\beta\le 0$, we show that $\Psi(u)=1$ for any $u\ge 0$.

## Suggested Citation

• Serguei Pergamenchtchikov & Zeitouny Omar, 2010. "Ruin probability in the presence of risky investments," Papers 1011.1329, arXiv.org.
• Handle: RePEc:arx:papers:1011.1329
as

File URL: http://arxiv.org/pdf/1011.1329

## References listed on IDEAS

as
1. Anna Frolova & Serguei Pergamenshchikov & Yuri Kabanov, 2002. "In the insurance business risky investments are dangerous," Finance and Stochastics, Springer, vol. 6(2), pages 227-235.
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