Skip to main content
Log in

Second-order asymptotics for the ruin probability in the case of very large claims

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. H. Cramer, “On some questions connected with mathematical risk,” Univ. California Publ. Statist.,2, 99–125 (1954).

    Google Scholar 

  2. W. Feller, An Introduction to Probability Theory and Its Applications. Vol. 2 [Russian translation], Mir, Moscow (1967).

    MATH  Google Scholar 

  3. A. A. Borovkov, Stochastic Processes in Queueing Theory [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  4. K. B. Athreya and P. E. Ney, Branching Processes, Springer-Verlag, Berlin, Heidelberg, and new York (1972).

    MATH  Google Scholar 

  5. A. G. Pakes, “On the tails of waiting-time distributions,” J. Appl. Probab.,15, 555–564 (1975).

    Article  Google Scholar 

  6. J. L. Teugels, “The class of subexponential distributions,” Ann. Probab.,3, 1000–1011 (1975).

    MATH  Google Scholar 

  7. N. Veraverbeke, “Asymptotic behaviour of Wiener-Hopf factors of a random walk,” Stochastic Process Appl.,5, 27–37 (1977).

    Article  MATH  Google Scholar 

  8. P. Embrechts and N. Veraverbeke, “Estimates for the ruin probability with special emphasis on the possibility of large claims,” Insurance Math. Econom.,1, 55–72 (1982).

    Article  MATH  Google Scholar 

  9. B. A. Rogozin, “An estimate of the remainder term in limit theorems of renewal theory,” Teor. Veroyatnost. i Primenen,18, No. 4, 703–717 (1973).

    Google Scholar 

  10. E. Omey and E. Willekens, “Second-order behaviour of the tail of a subordinated probability distribution,” Stochastic Process Appl.,21, 339–353 (1986).

    Article  MATH  Google Scholar 

  11. E. Omey and E. Willekens, “Second-order behaviour of distributions subordinate to a distribution with finite mean,” Comm. Statist. Stochastic Models, No, 3, 311–342 (1987).

    Article  MATH  Google Scholar 

  12. E. Willekens, Hogere Orde Theorie Voor Subexponentiele Verdelingen, Ph. D. Thesis, K. U. Leuven (1986).

  13. E. Willekens and J. L. Teugels, “Asymptotic expansions for waiting time probabilities inM|G|1 queue with long-tailed service time,” Queueing Systems Theory Appl.,10, No. 4, 295–311 (1992).

    Article  MATH  Google Scholar 

  14. A. Baltrūnas and E. Omey, “The rate of convergence for subexponential distribution,” Liet. Mat. Rink.,38, 1–18 (1998).

    Google Scholar 

  15. I. F. Pinelis, “On asymptotic equivalence of large deviation probabilities of the sum and maximum of independent random variables,” in: Limits Theorems [in Russian], Nauka Novosibirsk, 1985.

    Google Scholar 

  16. E. Willekens, “The structure of the class of subexponential distributions,” Probab. Theory Related Fields,77, 567–581 (1988).

    Article  MATH  Google Scholar 

  17. E. Omey, “On the difference between the product and the convolution product of distribution functions,” Publ. Inst. math. (Beograd) (N. S.),55, 111–145 (1994).

    MATH  Google Scholar 

Download references

Authors

Additional information

Vilnyus. Translated fromSibirskiĭ Matematicheskiĭ Zhurnal, Vol. 40, No. 6, pp. 1226–1235, November–December, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baltrunas, A. Second-order asymptotics for the ruin probability in the case of very large claims. Sib Math J 40, 1034–1043 (1999). https://doi.org/10.1007/BF02677526

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02677526

Keywords

Navigation