Interval estimation of the ruin probability in the classical compound Poisson risk model

Abstract

Estimating ruin probability is an important problem in insurance. Zhang et al. (2014) proposed a novel nonparametric estimation method for the ruin probability in the classical risk model with unknown claim size distribution, based on the Fourier transform and the kernel density estimation. However, asymptotic distributions of their estimators are unknown, which hampers statistical inference for the ruin probability. The authors establish asymptotic normal distributions of the estimators with known and with unknown intensity. Since the standard deviations of estimators are hard to estimate, a bootstrap method is advanced to estimate them. This allows one to construct a confidence interval estimate of the ruin probability. Furthermore, a new method is proposed to fast calculate the estimates, and the numerical results are stable and free of the “curse of large initial surplus” problem. Simulations are conducted to demonstrate nice finite sample performance of the estimators. A real dataset from a car insurance company is analyzed for illustrating the use of the proposed methodology.