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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.

MSC:

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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