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In the insurance business risky investments are dangerous

Listed author(s):
  • Anna Frolova

    (Alfa-Bank, Masha Poryvaeva str., 9, 107078, Moscow, Russia)

  • Serguei Pergamenshchikov

    (Tomsk State University, Lenin str., 36, 634050 Tomsk, Russia Manuscript)

  • Yuri Kabanov


    (Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon cedex, France and Central Economics and Mathematics Institute, Moscow, Russia)

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

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Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 6 (2002)
Issue (Month): 2 ()
Pages: 227-235

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Handle: RePEc:spr:finsto:v:6:y:2002:i:2:p:227-235
Note: received: January 2001; final version received: June 2001
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