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Estimating of the Renewal Function with Heavy-tailed Claims

Authors: Rassoul Abdelaziz


We develop a new estimator of the renewal function for heavy-tailed claims amounts. Our approach is based on the peak over threshold method for estimating the tail of the distribution with a generalized Pareto distribution. The asymptotic normality of an appropriately centered and normalized estimator is established, and its performance illustrated in a simulation study.

Keywords: generalized pareto distribution‎, peak-over-threshold, heavy-tailed distribution, Renewal function, POT method, extremes value

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