On the number of near-maximum insurance claims

A near-maximum claim size is one falling within a fixed distance a of the c urrent record claim size. In this paper we study the statistic K-t(a) count ing the number of near-maximum insurance claims in the time period [0, t]. Some distributional results of K-t(a) are considered, as well as asymptotic behaviours as E --> infinity . Subject to a limitation on the tail thickne ss of the claim-size law, these results provide an estimate of the long-ter m total value of near-maximum insurance claims. (C) 2001 Elsevier Science B ,V. All rights reserved.