Estimating the discounted density of the deficit at ruin by Fourier cosine series expansion

Abstract

In this paper, we study the statistical estimation of the discounted density of the deficit at ruin in the classical risk model. The estimator is constructed by the two-dimensional Fourier cosine series expansion. It is shown that the estimator is easily computed and has fast convergence rate. Some simulation results are presented to show that the estimator performs very well when the sample size is finite.