On a nonparametric estimator for ruin probability in the classical risk model

Abstract

In this paper, we present a nonparametric estimator for ruin probability in the classical risk model with unknown claim size distribution. We construct the estimator by Fourier inversion and kernel density estimation method. Under some conditions imposed on the kernel, bandwidth and claim size density, we present some large sample properties of the estimator. Some simulation studies are also given to show the finite sample performance of the estimator.

Estimating the Gerber-Shiu Expected Discounted Penalty Function for Lévy Risk Model

“…Over the past decade, the importance of statistical estimation of Gerber-Shiu function has advanced rapidly. As a special type of Gerber-Shiu functions, the ruin probability is estimated by Mnatsakanov et al [31], Masiello [32], and Zhang et al [33] under the classical compound Poisson risk model. Further, Zhang [34] and Yang et al [35] estimated the finite ruin probability by double Fourier transform.…”

Approximation of the ruin probability using the scaled Laplace transform inversion

“…See, for example, Gzyl et al [6], Avram et al [7], and Zhang et al [8] among others. A very interesting approximation based on the Trefethen–Weideman–Schmelzer (TWS) method (see [9]) is constructed in Albrecher et al [10].…”

Nonparametric estimate of the ruin probability in a pure-jump Lévy risk model

“…Thus, statistical methodology can be directly used to analyze the insurance's risk from the data. For more recent contributions on statistical estimate of the ruin probability, we refer the readers to Shimizu (2012), Masiello (2012) and Zhang et al (2012).…”

“…In Masiello (2012) and Zhang et al (2012), ruin probability for the classical risk model is estimated and the common key tool for estimation is the Pollaczeck-Khinchine formula. However, they use different approaches to treat the infinite sum of convolution powers in the Pollaczeck-Khinchine formula.…”

“…In Masiello (2012), empirical distribution is used to estimate the convolution powers (see also Frees (1986)). Zhang et al (2012) apply Fourier method to transform the infinite sum of convolutions to a single integral and then estimate the claim size distribution by kernel method. In this paper we will estimate the ruin probability in the pure-jump Lévy risk model (1.1) that includes the classical risk model as a special case.…”