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Large Deviations of HeavyTailed Sums with Applications in Insurance
 T. Mikosch,
 A.V. Nagaev
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First we give a short review of large deviation results for sums of i.i.d. random variables. The main emphasis is on heavytailed 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.
This revised version was published online in July 2006 with corrections to the Cover Date.
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 Title
 Large Deviations of HeavyTailed Sums with Applications in Insurance
 Journal

Extremes
Volume 1, Issue 1 , pp 81110
 Cover Date
 19980101
 DOI
 10.1023/A:1009913901219
 Print ISSN
 13861999
 Online ISSN
 1572915X
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 large deviation
 heavy tails
 shot noise
 total claim amount
 Cramér–Lundberg model
 reinsurance
 ruin probability
 Authors

 T. Mikosch ^{(1)}
 A.V. Nagaev ^{(2)}
 Author Affiliations

 1. Department of Mathematics, University of Groningen, P.O. Box 800, NL9700 AV, Groningen, The Netherlands
 2. Faculty of Mathematics, and Informatics, Copernicus University, ul, Chopina 12/18, 87100, Torun, Poland