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

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  • Yuan Gao

    (School of Mathematical Sciences, Qufu Normal University, Jining 273165, China)

  • Honglong You

    (School of Statistics, Qufu Normal University, Jining 273165, China)

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.

Suggested Citation

  • Yuan Gao & Honglong You, 2021. "The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered α -Stable Lévy Subordinator," Mathematics, MDPI, vol. 9(21), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2654-:d:660804
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    References listed on IDEAS

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