Estimating the Gerber–Shiu function in the perturbed compound Poisson model by Laguerre series expansion
Estimating the Gerber–Shiu function in the perturbed compound Poisson model by Laguerre series expansion
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DOI：
10.1016/j.jmaa.2018.09.033
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发表时间：
2019-01
影响因子：
1.3
通讯作者：
Wen Su;Yaodi Yong;Zhimin Zhang
中科院分区：
文献类型：
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作者：
Wen Su;Yaodi Yong;Zhimin Zhang
在本文中，我们研究了受扩散扰动的复合泊松风险模型中 Gerber-Shiu 函数的统计估计。这个问题在[32]中已经通过 Fourier-Sinc 级数展开方法解决了。与[32]不同的是，我们使用Laguerre级数来扩展Gerber-Shiu函数并提出了相关的估计量。该估计器计算简单且收敛速度快。提出了各种模拟研究来确认当样本量有限时估计器表现良好。
In this paper, we study the statistical estimation of the Gerber–Shiu function in the compound Poisson risk model perturbed by diffusion. This problem has been solved in [32] by the Fourier–Sinc series expansion method. Different from [32], we use the Laguerre series to expand the Gerber–Shiu function and propose a relevant estimator. The estimator is easily computed and has fast convergence rate. Various simulation studies are presented to confirm that the estimator performs well when the sample size is finite.