Cybernetics and Systems Analysis

, Volume 54, Issue 2, pp 242–248 | Cite as

On the Continuous Dependence of Non-Ruin Probability on Claim Distribution Function in the Classical Risk Model

Article
  • 3 Downloads

Abstract

The Cramer–Lundberg model is considered as a model of insurance company. Since it is impossible to obtain an explicit solution for the non-ruin probability function of insurance company for an arbitrary distribution of the values of insurance claims, the authors consider the problem of estimating the convergence of the original non-ruin probability to one that would be obtained by approximating the values of claim distribution function.

Keywords

Cramer–Lundberg model risk process convergence ruin probability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. I. Lundberg, Approximerad Framstallning av Sannolikhetsfunktionen, II. Aterforsakring av Kollektivrisker, Almqvist & Wiksell, Uppsala (1903).Google Scholar
  2. 2.
    F. I. Lundberg, Forsakringsteknisk Riskutjamning, F. Englunds boktryckeri A. B., Stockholm (1926).Google Scholar
  3. 3.
    R. E. Beard, T. Pentikainen, and E. Pesonen, Risk Theory. The Stochastic Basis of Insurance, Chapman and Hall, London–New York (1984).MATHGoogle Scholar
  4. 4.
    M. M. Leonenko, Yu. S. Mishura, V. M. Parkhomenko, and M. J. Yadrenko, Probability-Theoretic and Statistical Methods in Econometrics and Financial Mathematics [in Ukrainian], Informtekhnika, Kyiv (1995).Google Scholar
  5. 5.
    S. Assmussen and H. Albrecher, Ruin Probabilities, Advanced Series on Statistical Science & Applied Probability, Vol. 14, World Scientific, Singapore (2010).Google Scholar
  6. 6.
    B. V. Bondarev and T. V. Zhmykhova, “Insurance company’s non-ruin probability for the Cramer–Lundberg model and G-distributed claim,” Prykladna Statystyka. Aktuarna ta Finansova Matem., No. 1–2, 54–70 (2005).Google Scholar
  7. 7.
    B. V. Bondarev and V. O. Boldyreva, “Approximation of non-ruin probability for the Cramer-Lundberg model,” Prykladna Statystyka. Aktuarna ta Finansova Matem., No. 1, 13–22 (2012).Google Scholar
  8. 8.
    A. V. Tymko, “Approximation of the distribution of a positive random variable by a mixture of shifted exponential distributions,” Visnyk Donetsk. Univer., Ser. A: Pryrodnychi Nauky, Issue 1, 20–25 (2006).Google Scholar
  9. 9.
    V. O. Boldyreva, “Modeling and analysis of the activity of insurance companies on (B, S)-market,” Author’s Abstract of Ph.D. Theses, V. M. Glushkov Inst. of Cybernetics, NAS of Ukraine, Kyiv (2015).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Vasyl’ Stus Donetsk National UniversityVinnytsiaUkraine
  2. 2.Taras Shevchenko National University of KyivKyivUkraine

Personalised recommendations