POT-Based Estimation of the Renewal Function of Interoccurrence Times of Heavy-Tailed Risks - Abdelhakim Necir; Abdelaziz Rassoul; Djamel Meraghni (Journal of Probability and Statistics)
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.