Nonparametric estimation of some dividend problems by Fourier sinc series expansion in the Wiener-Poisson risk model

Abstract

In this paper, we consider some dividend problems in the perturbed compound Poisson risk model (Wiener Process) under constant barrier dividend strategy. We use the Fourier-sinc method to propose the estimators of the expected present dividend payments before ruin and the expected discounted penalty function also called Gerber-Shiu function using a random sample on claim number, individual claim sizes and surplus flow level. We show that our estimators have good convergence rate. We also derive some simulation examples to show the effectiveness of the estimators under finite sample. We simulate many graphs of ours estimators to show that show that our estimators are very closed and converge to the real curve.