An Estimator For The Gerber-Shiu Function Using The Fourier-Sinc Series

The main research content of this paper is learning how to use the Sinc estimation method to put forward a non-parametric estimation of the Gerber-Shiu function about discrete observation data.Firstly,this paper introduces the necessity of the emergence of the insurance industry from the perspective of the objective characteristics of risk,and briefly introduces the related knowledge as well as the research status at home and abroad of bankruptcy probability,classic risk model,the Gerber-Shiu function and the Sinc estimation method.Then,on the basis of preliminary knowledge,this paper introduces the way to use the Sinc estimation method to estimate the Gerber-Shiu function based on discrete information of earnings process and accumulated claim process,and gives specific estimation steps.In addition,this paper illustrates the estimation effect of the estimation method through theoretical proof and numerical simulation respectively.In the part of numerical simulation,in order to better illustrate the universality and good applicability of the estimation method,this paper respectively simulates and compares four kinds of risk problems obtained by the Gerber-Shiu function with the truth value under the assumption that claims obey exponential distribution and Erlang(2)distribution respectively.The results show that the Sinc estimation method has a very efficient convergence rate and accuracy.At the same time,this paper also compares the estimation effect of Sinc estimation method with that of some other estimation method in another paper,and finds that the estimation effect of the Sinc estimation method is relatively unchanged with the change of initial surplus,and the estimation effect is obviously better when the initial surplus is large.Finally,by selecting different parameters,this paper also obtains a very practical feature that the data observation time interval required by the Sinc estimation method is relatively short.In general,this paper not only gives the train of thought and specific derivation process of estimating the Gerber-Shiu function by the Sinc estimation method,but also compares the research results with the research results of some other paper in numerical simulation to illustrate the advancement of the Sinc estimation method.The Sinc estimation method is not widely used in the field of financial risk in the current research results.The proposed method in this paper can well demonstrate the good approximate effect of this estimation method and provide a reference for more relevant studies.