Nonparametric estimation of ruin probability by complex Fourier series expansion in the compound Poisson model

Abstract

In this paper, we consider the estimation of ruin probability in the classical compound Poisson model. We first show that the ruin probability can be expressed by the complex Fourier series expansion. Then using a random sample on claim number and individual claim sizes we construct a nonparametric estimator of the ruin probability. Error analysis of the new estimator is made when the sample size is large, and simulation results are also provided to show the efficiency of our method when the sample size is finite.