Journal of Probability and Statistics
Volume 2010 (2010), Article ID 965672, 14 pages
doi:10.1155/2010/965672
Research Article

POT-Based Estimation of the Renewal Function of Interoccurrence Times of Heavy-Tailed Risks

Abdelhakim Necir,1 Abdelaziz Rassoul,2 and Djamel Meraghni1

1Laboratory of Applied Mathematics, University Mohamed Khider, P.O. Box 145, Biskra 07000, Algeria
2Ecole Nationale Superieure d'Hydraulique, Guerouaou, BP 31, Blida 09000, Algeria

Received 13 October 2009; Accepted 24 February 2010

Academic Editor: Ričardas Zitikis

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.

Abstract

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.