, Volume 1, Issue 1, pp 81–110

Large Deviations of Heavy-Tailed Sums with Applications in Insurance

  • T. Mikosch
  • A.V. Nagaev

DOI: 10.1023/A:1009913901219

Cite this article as:
Mikosch, T. & Nagaev, A. Extremes (1998) 1: 81. doi:10.1023/A:1009913901219


First we give a short review of large deviation results for sums of i.i.d. random variables. The main emphasis is on heavy-tailed distributions. We stress more the methodology than the detailed calculations. Large deviation techniques are then applied to randomly indexed sums and shot noise processes. We also indicate the close relationship between large deviation results and the modeling of large insurance claims.

large deviationheavy tailsshot noisetotal claim amountCramér–Lundberg modelreinsuranceruin probability

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • T. Mikosch
    • 1
  • A.V. Nagaev
    • 2
  1. 1.Department of MathematicsUniversity of GroningenGroningenThe Netherlands
  2. 2.Faculty of Mathematics, and InformaticsCopernicus University, ulTorunPoland