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Making use of the peaks over threshold (POT) estimation method,we propose a semiparametric estimator for the renewal function ofinteroccurrence times of heavy-tailed insurance claims with infinitevariance. We prove that the proposed estimator is consistent andasymptotically 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 renewalfunction of dangerous risks

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