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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Yuan Gao, Honglong You
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	ruin probability spectrally negative Lévy process Fourier transform high-frequency data Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/95a83d3ea8b54a17a1752e49dfc6878a
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:95a83d3ea8b54a17a1752e49dfc6878a
record_format	dspace
spelling	oai:doaj.org-article:95a83d3ea8b54a17a1752e49dfc6878a2021-11-11T18:13:53ZThe Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator10.3390/math92126542227-7390https://doaj.org/article/95a83d3ea8b54a17a1752e49dfc6878a2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2654https://doaj.org/toc/2227-7390In 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.Yuan GaoHonglong YouMDPI AGarticleruin probabilityspectrally negative Lévy processFourier transformhigh-frequency dataMathematicsQA1-939ENMathematics, Vol 9, Iss 2654, p 2654 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	ruin probability spectrally negative Lévy process Fourier transform high-frequency data Mathematics QA1-939
spellingShingle	ruin probability spectrally negative Lévy process Fourier transform high-frequency data Mathematics QA1-939 Yuan Gao Honglong You The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator
description	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.
format	article
author	Yuan Gao Honglong You
author_facet	Yuan Gao Honglong You
author_sort	Yuan Gao
title	The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator
title_short	The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator
title_full	The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator
title_fullStr	The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator
title_full_unstemmed	The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered <i>α</i>-Stable Lévy Subordinator
title_sort	speed of convergence of the threshold estimator of ruin probability under the tempered <i>α</i>-stable lévy subordinator
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/95a83d3ea8b54a17a1752e49dfc6878a
work_keys_str_mv	AT yuangao thespeedofconvergenceofthethresholdestimatorofruinprobabilityunderthetemperediaistablelevysubordinator AT honglongyou thespeedofconvergenceofthethresholdestimatorofruinprobabilityunderthetemperediaistablelevysubordinator AT yuangao speedofconvergenceofthethresholdestimatorofruinprobabilityunderthetemperediaistablelevysubordinator AT honglongyou speedofconvergenceofthethresholdestimatorofruinprobabilityunderthetemperediaistablelevysubordinator
_version_	1718431900345827328

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

Ejemplares similares