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Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model

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School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
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Mathematics 2020, 8(10), 1638; https://doi.org/10.3390/math8101638
Received: 8 July 2020 / Revised: 1 August 2020 / Accepted: 10 August 2020 / Published: 23 September 2020
(This article belongs to the Special Issue Stochastic Statistics and Modeling)
Nonparametric estimation of the Gerber-Shiu function is a popular topic in insurance risk theory. Zhang and Su (2018) proposed a novel method for estimating the Gerber-Shiu function in classical insurance risk model by Laguerre series expansion based on the claim number and claim sizes of sample. However, whether the estimators are asymptotically normal or not is unknown. In this paper, we give the details to verify the asymptotic normality of these estimators and present some simulation examples to support our result. View Full-Text
Keywords: Gerber-Shiu function; Laguerre series; classical risk model; asymptotic normality Gerber-Shiu function; Laguerre series; classical risk model; asymptotic normality
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MDPI and ACS Style

Su, W.; Yu, W. Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model. Mathematics 2020, 8, 1638. https://doi.org/10.3390/math8101638

AMA Style

Su W, Yu W. Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model. Mathematics. 2020; 8(10):1638. https://doi.org/10.3390/math8101638

Chicago/Turabian Style

Su, Wen, and Wenguang Yu. 2020. "Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model" Mathematics 8, no. 10: 1638. https://doi.org/10.3390/math8101638

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