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.
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