Nonparametric estimate of the ruin probability in a pure-jump Lévy risk model. (English) Zbl 1284.62245

Summary: We propose a nonparametric estimator of ruin probability in a Lévy risk model. The aggregate claims process \(X=\{X_t,\geq 0\}\) 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.


62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
91B30 Risk theory, insurance (MSC2010)
60G51 Processes with independent increments; Lévy processes
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