The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator

Abstract

In this paper, a nonparametric estimator of ruin probability is introduced in a spectrally negative Lévy process where the jump component is a tempered α-stable subordinator. Given a discrete record of high-frequency data, a threshold technique is proposed to estimate the mean of the jump size and use the Fourier transform and the Pollaczek–Khinchin formula to construct the estimator of ruin probability. The convergence rate of the integrated squared error for the estimator is studied.

Keywords

• ruin probability
• spectrally negative Lévy process
• Fourier transform
• high-frequency data