TITLE:
Estimating the Gerber-Shiu Function by Fourier Cosine Series Expansion in the Wiener-Poisson Risk Model
AUTHORS:
Marcelin Romeo Noumegni Kenmoe, Jane Akinyi Aduda, Mbele Bidima Martin Le Doux
KEYWORDS:
COS Method, Perturbed Compound Poisson Risk Model, Surplus, Claim Sizes, Claim Number, Gerber-Shiu, Ruin, Poisson Process, Expected Discounted Penalty Function
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.13 No.3,
July
31,
2023
ABSTRACT: 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.