Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Abstract

This paper considers the estimation of ruin probability in an insurance risk model with stochastic premium income. We first show that the ruin probability can be approximated by the complex Fourier series (CFS) expansion method. Then, we construct a nonparametric estimator of the ruin probability and analyze its convergence. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

Keywords

• compound Poisson insurance risk model
• stochastic processes
• ruin probability
• nonparametric estimation
• complex Fourier series expansion