The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator
In this paper, a nonparametric estimator of ruin probability is introduced in a spectrally negative Lévy process where the jump component is a tempered <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</m...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/95a83d3ea8b54a17a1752e49dfc6878a |
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| Sumario: | In this paper, a nonparametric estimator of ruin probability is introduced in a spectrally negative Lévy process where the jump component is a tempered <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-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. |
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