Skip to main content

In the insurance business risky investments are dangerous


We find an exact asymptotics of the ruin probability \(\Psi (u)\) when the capital of insurance company is invested in a risky asset whose price follows a geometric Brownian motion with mean return a and volatility \(\sigma>0\). In contrast to the classical case of non-risky investments where the ruin probability decays exponentially as the initial endowment u tends to infinity, in this model we have, if \(\rho:=2a/\sigma^2>1\), that \(\Psi(u)\sim Ku^{1-\rho}\) for some \(K>0\). If \(\rho<1\), then \(\Psi(u)=1\).

This is a preview of subscription content, access via your institution.

Author information



Additional information

Manuscript received: January 2001; final version received: June 2001

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Frolova, A., Kabanov, Y. & Pergamenshchikov, S. In the insurance business risky investments are dangerous. Finance Stochast 6, 227–235 (2002).

Download citation

  • Key words: Risk process, geometric Brownian motion, ruin probabilities
  • JEL Classification: G22, G23
  • Mathematics Subject Classification (1991): 62P05,60J25