On a Nonparametric Estimator for the Finite Time Survival Probability with Zero Initial Surplus

In this paper, we consider the estimation of the finite time survival probability in the classical risk model when the initial surplus is zero. We construct a nonparametric estimator by Fourier inversion and kernel density estimation method. Under some mild assumptions imposed on the kernel, bandwid...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 32; no. 3; pp. 739 - 754
Main Authors Zhang, Zhi-min, Yang, Hai-liang, Yang, Hu
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2016
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Asymptotic properties
Computer simulation
Estimating techniques
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonparametric statistics
Normality
Risk
Survival
Theoretical
估计方法
古典风险模型
有限时间
有限样本
渐近正态性
生存概率
盈余
非参数估计
asymptotic normality
finite time survival probability
variance
kernel
bias
fourier transform
91B30
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Summary:In this paper, we consider the estimation of the finite time survival probability in the classical risk model when the initial surplus is zero. We construct a nonparametric estimator by Fourier inversion and kernel density estimation method. Under some mild assumptions imposed on the kernel, bandwidth and claim size density, we derive the order of the bias and variance, and show that the estimator has asymptotic normality property. Some simulation studies show that the estimator performs quite well in the finite sample setting.
Bibliography:finite time survival probability; fourier transform; kernel; bias; variance; asymptotic normality
11-2041/O1
In this paper, we consider the estimation of the finite time survival probability in the classical risk model when the initial surplus is zero. We construct a nonparametric estimator by Fourier inversion and kernel density estimation method. Under some mild assumptions imposed on the kernel, bandwidth and claim size density, we derive the order of the bias and variance, and show that the estimator has asymptotic normality property. Some simulation studies show that the estimator performs quite well in the finite sample setting.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-016-0601-x