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Advances in Stochastic Models for Reliability, Quality and Safety pp 67–80Cite as

Investigation of Convergence Rates in Risk Theory in the Presence of Heavy Tails

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Abstract

Asmussen and Klüppelberg (1996) established limit theorems for various random variables occurring in risk theory. In the present paper rates of convergence in certain limit theorems are given, which may be improved in some special cases.

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References

  1. Asmussen, S. and Klüppelberg, C. (1996). Large deviations results in the presence of heavy tails, with applications to insurance risk, Stochastic Processes and Applications, 64, 103–125.

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  4. Goldie, C. M. and Resnick, S. (1988). Distributions that are both subex-ponential and in the domain of attraction of an extreme-value distribution, Advances in Applied Probability, 20, 706–718.

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  5. Pitman, E. J. G. (1980). Subexponential distribution functions, Journal of the Australian Mathematics Society, Series A, 29, 337–347.

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Author information

Authors and Affiliations

  1. Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Simone Liebner

Authors
  1. Simone Liebner
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Editor information

Editors and Affiliations

  1. Dept. of Mathematical Stochastics, Otto-von-Guericke-University Magdeburg, Box 4120, D-39016, Magdeburg, Germany

    Waltraud Kahle

  2. Dept. of Applied Mathematics, University of Würzburg, Sanderring 2, D-97070, Würzburg, Germany

    Elart von Collani

  3. Department of Mathematical Stochastics, Technical University Dresden, Zellescher Weg 12-14, D-01069, Dresden, Germany

    Jürgen Franz

  4. Department of Stochastics, University of Ulm, D-89069, Ulm, Germany

    Uwe Jensen

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© 1998 Birkhäuser Boston

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Liebner, S. (1998). Investigation of Convergence Rates in Risk Theory in the Presence of Heavy Tails. In: Kahle, W., von Collani, E., Franz, J., Jensen, U. (eds) Advances in Stochastic Models for Reliability, Quality and Safety. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2234-7_5

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  • DOI: https://doi.org/10.1007/978-1-4612-2234-7_5

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7466-7

  • Online ISBN: 978-1-4612-2234-7

  • eBook Packages: Springer Book Archive

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