Journal of Mathematical Sciences

, Volume 93, Issue 4, pp 609–611 | Cite as

The Cramér condition is necessary and sufficient for asymptotically exponential decrease of ruin probability

  • O. P. Vinogradov
Article

Abstract

It is shown that the Cramér condition is necessary and sufficient for asymptotically exponential decrease of ruin probability.

Keywords

Exponential Decrease 

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References

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    O. P. Vinogradov, “On an age-dependent branching process,”Teor. Veroyatn. Primen.,9, No. 1, 146–152 (1964).MATHGoogle Scholar
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    T. E. Harris,The Theory of Branching Processes, Springer, Berlin (1963).Google Scholar
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    P. Embrechts and C. Klüppelberg, “Some aspects of insurance mathematics,”Theor. Probab. Appl.,38, No. 2, 374–417 (1993).Google Scholar
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    W. Feller,An Introduction to Probability Theory and Its Applications, New York (1971).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • O. P. Vinogradov
    • 1
  1. 1.Department of Probability Theory, Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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