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

Author

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  • Abdelhakim Necir
  • Abdelaziz Rassoul
  • Djamel Meraghni

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.

Suggested Citation

  • Abdelhakim Necir & Abdelaziz Rassoul & Djamel Meraghni, 2010. "POT-Based Estimation of the Renewal Function of Interoccurrence Times of Heavy-Tailed Risks," Journal of Probability and Statistics, Hindawi, vol. 2010, pages 1-14, May.
    • Handle: RePEc:hin:jnljps:965672
    DOI: 10.1155/2010/965672
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