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

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.