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

الملخص EN

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.