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Xie, J.Y. and Zhang, Z.M. (2022) Recursive Approximating to the Finite-Time Gerber-Shiu Function in Lévy Risk Models under Periodic Observation. Journal of Computational and Applied Mathematics, 399, Article ID: 113703.
https://doi.org/10.1016/j.cam.2021.113703

has been cited by the following article:

• 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.