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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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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
  4. 4.
    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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