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In the insurance business risky investments are dangerous

Author

Listed:
  • 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)

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

Suggested Citation

  • 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.
    • 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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    More about this item

    Keywords

    Risk process; geometric Brownian motion; ruin probabilities;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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