## 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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### References:

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