, Volume 1, Issue 1, pp 81-110

Large Deviations of Heavy-Tailed Sums with Applications in Insurance

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Abstract

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.

This revised version was published online in July 2006 with corrections to the Cover Date.