%0 Journal Article
%T Estimating the Gerber-Shiu Function by Fourier Cosine Series Expansion in the Wiener-Poisson Risk Model
%A Marcelin Romeo Noumegni Kenmoe
%A Jane Akinyi Aduda
%A Mbele Bidima Martin Le Doux
%J Journal of Mathematical Finance
%P 271-283
%@ 2162-2442
%D 2023
%I Scientific Research Publishing
%R 10.4236/jmf.2023.133017
%X Gerber-Shiu function is the joint distribution of the time to ruin, the surplus before ruin and the deficit at ruin. In this paper, we propose a non-parametric estimator of the expected discounted penalty function; the Gerber-Shiu function for a compound Poisson risk model perturbed by diffusion is also called the Wiener-Poisson risk model. The estimator is based on the Fourier cosine series expansion method. It shows that our estimator has a fast convergence rate. We also derived some simulation examples to show the effectiveness of the estimator under a finite sample.
%K COS Method
%K Perturbed Compound Poisson Risk Model
%K Surplus
%K Claim Sizes
%K Claim Number
%K Gerber-Shiu
%K Ruin
%K Poisson Process
%K Expected Discounted Penalty Function
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=126714