Large deviations of heavy-tailed random sums with applications in insurance and finance

Abstract

We prove large deviation results for the random sum , , where are non-negative integer-valued random variables and are i.i.d. non-negative random variables with common distribution function F, independent of . Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function F is supposed to be of Pareto type (regularly or extended regularly varying). The large deviation results are applied to certain problems in insurance and finance which are related to large claims.