Non-Parametric Threshold Estimation for the Wiener–Poisson Risk Model

Abstract

In this paper, we consider the Wiener–Poisson risk model, which consists of a Wiener process and a compound Poisson process. Given the discrete record of observations, we use a threshold method and a regularized Laplace inversion technique to estimate the survival probability. In addition, we also construct an estimator for the distribution function of jump size and study its consistency and asymptotic normality. Finally, we give some simulations to verify our results.

Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion

“…However, their probabilistic characteristics are usually unknown to the insurer. To relax the restriction on claim size distributions, Shimizu [9,10], You and Cai [11], You and Yin [12], You et al [13], You and Gao [14], Cai et al [15] estimated the Gerber-Shiu function by Laplace transform. Zhang [16,17], Shimizu and Zhang [18], Zhang [19] considered estimating the Gerber-Shiu function by Fourier transform.…”