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Non-parametric estimation for a pure-jump Lévy process

Published online by Cambridge University Press:  10 May 2017

Chunhao Cai ,
Junyi Guo  and
Honglong You
Chunhao Cai
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, China
Junyi Guo
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, China
Honglong You*
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, China
*
*Correspondence to: Honglong You, School of Mathematical Sciences, Nankai University, Tianjin 300071, China. Tel: 0086-13212002912. E-mail: youhonglong815@163.com
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Abstract

In this paper, we propose an estimator of the survival probability for a Lévy risk model observed at low frequency. The estimator is constructed via a regularised version of the inverse of the Laplace transform. The convergence rate of the estimator in a sense of the integrated squared error is studied for large sample size. Simulation studies are also given to show the finite sample performance of our estimator.

Keywords

Survival probabilityNon-parametric estimationLaplace transformLévy process

JEL classification

G22: Insurance • Insurance Companies • Actuarial Studies C14: Semiparametric and Nonparametric Methods: General
Type
Paper
Information
Annals of Actuarial Science , Volume 12 , Issue 2 , September 2018 , pp. 338 - 349
Copyright
© Institute and Faculty of Actuaries 2017 

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