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

Abstract

This paper studies the statistical estimation of the Gerber-Shiu discounted penalty functions in a general spectrally negative Lévy risk model. Suppose that the claims process and the surplus process can be observed at a sequence of discrete time points. Using the observed data, the Gerber-Shiu functions are estimated by the Laguerre series expansion method. Consistent properties are studied under the large sample setting, and simulation results are also presented when the sample size is finite.

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

“…Wang et al [13,14] estimated the Gerber-Shiu function and the expected discounted penalty function in a compound Poisson insurance risk model with stochastic premium income. Huang et al [15] estimated the Gerber-Shiu expected discounted penalty function for Lévy risk model. For approximating the ruin probability and other risk measures, there are also some other methods.…”

Randomized observation periods for compound Poisson risk model with capital injection and barrier dividend

“…represents the Laplace transformation of the ruin time. The relevant references of Gerber-Shiu function can be found in Gerber and Shiu [33], Lin et al [34], Willmot and Dickson [35], Li et al [36], Huang et al [37], Zhang and Su [38], Preischl and Thonhauser [39], Zhang et al [40], and Palmowski and Vatamidou [41].…”

On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

“…Since then, it has become a standard tool for studying ruin related quantities. We refer the interested readers to Lin et al [40], Huang and Yu [41], Ruan et al [42], Li et al [43], Wang et al [44], Yang et al [45], Yu [46,47], Yuen et al [48], Huang et al [49], Xie and Zou [50].…”