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

Abstract

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.

Keywords

• Gerber-Shiu function
• Laguerre series
• classical risk model
• asymptotic normality