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In the insurance business risky investments are dangerous

Abstract.

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 \(\Psi(u)=1\).

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

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Frolova, A., Kabanov, Y. & Pergamenshchikov, S. In the insurance business risky investments are dangerous. Finance Stochast 6, 227–235 (2002). https://doi.org/10.1007/s007800100057

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