On a nonparametric estimator for the finite time survival probability with zero initial surplus

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• 作者：Zhi-min Zhang ; Hai-liang Yang ; Hu Yang
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：32
• 期：3
• 页码：739-754
• 全文大小：513 KB
• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932
• 卷排序：32

文摘

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.Keywordsfinite time survival probabilityfourier transformkernelbiasvarianceasymptotic normality