Copyright © 2010 Abdelhakim Necir et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Making use of the peaks over threshold (POT) estimation method,
we propose a semiparametric estimator for the renewal function of
interoccurrence times of heavy-tailed insurance claims with infinite
variance. We prove that the proposed estimator is consistent and
asymptotically normal, and we carry out a simulation study to compare its finite-sample behavior with respect to the nonparametric one.
Our results provide actuaries with confidence bounds for the renewal
function of dangerous risks.