Doklady Mathematics

, Volume 98, Issue 3, pp 622–625 | Cite as

Approximations in the Problem of Level Crossing by a Compound Renewal Process

  • V. K. Malinovskii


The classical problem of level crossing by a compound renewal process is considered, which has been extensively studied and has various applications. For the distribution of the first level crossing time, a new approximation is proposed, which is valid under minimal conditions and is obtained by applying a new method. It has a number of advantages over previously known approximations.


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  1. 1.
    S. Asmussen, Scand. Actuarial J. 1984, 31–57 (1984); Scand. Actuarial J. 1985, 57 (1985).CrossRefGoogle Scholar
  2. 2.
    S. Asmussen and H. Albrecher, Ruin Probabilities (World Scientific, Singapore, 2010).CrossRefzbMATHGoogle Scholar
  3. 3.
    B. von Bahr, Scand. Actuarial J. 1974, 190–204 (1974).CrossRefGoogle Scholar
  4. 4.
    K. Borovkov and D. C. M. Dickson, Insurance Math. Econ. 42, 1104–1108 (2008).CrossRefGoogle Scholar
  5. 5.
    S. Drekic and G. E. Willmot, ASTIN Bull. 33 (1), 11–21 (2003).MathSciNetCrossRefGoogle Scholar
  6. 6.
    J. M. A. Garcia, ASTIN Bull. 35 (1), 113–130 (2005).MathSciNetCrossRefGoogle Scholar
  7. 7.
    V. K. Malinovskii, Insurance Math. Econ. 22, 123–138 (1998).MathSciNetCrossRefGoogle Scholar
  8. 8.
    V. K. Malinovskii, “On the time of first level crossing and inverse Gaussian distribution,” (2017). Scholar
  9. 9.
    V. K. Malinovskii, “Generalized inverse Gaussian distributions and the time of first level crossing” (2017). Scholar
  10. 10.
    V. K. Malinovskii and K. V. Malinovskii, “On approximations for the distribution of first level crossing time” (2017). Scholar
  11. 11.
    J. L. Teugels, Insurance Math. Econ. 1, 163–175 (1982).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Central Economics and Mathematics InstituteRussian Academy of SciencesMoscowRussia

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