Quality of the Approximation of Ruin Probabilities Regarding to Large Claims

  • Aicha Bareche
  • Mouloud Cherfaoui
  • Djamil Aïssani
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 358)

Abstract

The aim of this work is to show, on the basis of numerical examples based on simulation results, how the strong stability bound on ruin probabilities established by Kalashnikov (2000) is affected regarding to different heavy-tailed distributions.

Keywords

Approximation Risk model Ruin probability Strong stability Large claim 

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References

  1. 1.
    Asmussen, S.: Ruin Probabilities. World Scientific, Singapore (2000)Google Scholar
  2. 2.
    Beirlant, J., Rachev, S.T.: The problems of stability in insurance mathematics. Insurance Math. Econom. 6, 179–188 (1987)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Buch-Larsen, T., Nielsen, J.P., Guillen, M., Bolancé, C.: Kernel density estimation for heavy-tailed distribution using the Champernowne transformation. Statistics 6, 503–518 (2005)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Coles, S.: An Introduction to Statistical Modelling of Extreme Values. Springer, Berlin (2001)CrossRefMATHGoogle Scholar
  5. 5.
    Embrechts, P., Klueppelberg, C., Mikosch, T.: Modelling Extremal Events for Finance and Insurance. Springer, Heidelberg (1997)CrossRefMATHGoogle Scholar
  6. 6.
    Embrechts, P., Veraverbeke, N.: Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance: Math. Econom. 1, 55–72 (1982)MathSciNetMATHGoogle Scholar
  7. 7.
    Kalashnikov, V.V.: The stability concept for stochastic risk models. Working Paper Nr 166, Laboratory of Actuarial Mathematics. University of Copenhagen (2000)Google Scholar
  8. 8.
    Kartashov, N.V.: Strong Stable Markov chains. TbiMC Scientific Publishers, VSPV, Utrecht (1996)MATHGoogle Scholar
  9. 9.
    Konstantinidis, D.G.: Comparison of ruin probability estimates in the presence of heavy tails. Journal Mathem 93, 552–562 (1999)MathSciNetMATHGoogle Scholar
  10. 10.
    Konstantinidis, D.G.: Risk models with extremal subexponentiality. Brazilian Journal of Probability and Statistics, Brazilian Statistical Association 21, 63–83 (2007)MathSciNetMATHGoogle Scholar
  11. 11.
    Panjer, H.H., Willmot, G.E.: Insurance Risk Models. The Society of Actuaries (1992)Google Scholar
  12. 12.
    Tsitsiashvili, G., Konstantinides, D.G.: Supertails in risk theory. Far Eastern Mathem. J. 2, 68–76 (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Aicha Bareche
    • 1
  • Mouloud Cherfaoui
    • 1
  • Djamil Aïssani
    • 1
  1. 1.Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of TechnologyUniversity of BejaiaBejaiaAlgeria

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