Estimating the Gerber–Shiu function in the perturbed compound Poisson model by Laguerre series expansion

摘要

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 by the Fourier–Sinc series expansion method. Different from , 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.