Nonparametric estimate of the ruin probability in a pure-jump Lévy risk model

In this paper, we propose a nonparametric estimator of ruin probability in a Lévy risk model. The aggregate claims process X={Xt,≥0} is modeled by a pure-jump Lévy process. Assume that high-frequency observed data on X are available. The estimator is constructed based on the Pollaczek-Khinchin formula and Fourier transform. Risk bounds as well as a data-driven cut-off selection methodology are presented. Simulation studies are also given to show the finite sample performance of our estimator.