Nonparametric Estimation Of Risk Models Under The Barrier Dividend Strategy

The statistical estimation of insurance actuarial quantities has become a hot topic in the research of risk theory,which has received extensive attention,and its significant advantages are gradually highlighted.On the one hand,the use of nonparametric estimation does not depend on specific models,which can measure risks more accurately and more in line with the actual risk situation of insurance companies,breaking the limitations of traditional probability analysis methods;on the other hand,nonparametric statistical methods have the characteristics of small errors and high degree of fit,which can be widely used in actual risk situations.In recent years,the use of nonparametric statistical methods to study insurance actuarial quantities has achieved certain results in various risk models.For nonparametric statistics,commonly used statistical methods' are Laplace(inverse)transformation method,Fourier(inverse)transformation method,nuclear density estimation method,Fourier-Sinc series expansion method,Fourier-Cosine series expansion method,Laguerre series expansion method,Complex Fourier series expansion method(abbreviated as CFS expansion method)etc,among them,CFS expansion method is a relatively new estimation method in the study of nonparametric statistical of actuarial quantity.The issue of dividends is one of the important research topics in the field of insurance actuarial.Among them,the Barrier dividend strategy is a more widely used,more thoroughly researched,and more maturely developed dividend strategy.It not only provides a certain theoretical basis for the profitability operation mechanism of insurance companies,but also broadened the direction of research and promoted the development of the insurance actuarial discipline,so it has important research value and scientific research significance.Based on the current research status of nonparametric statistical methods and Barrier dividend strategy,this paper applies the CFS expansion method to the risk model with Bar-rier dividend strategy,and gives the estimator and its error analysis and stability research.Structure of the article consists of five parts:the first part introduces the background and significance of the article research,and analyzes the research status of nonparametric s-tatistics and risk models at home and abroad;the second part introduces the classic risk models with dividends and the CFS nonparametric statistical method,deduces the nonpara-metric estimation expression of Gerber-Shiu function (?)_b(u);the third part studies the error|(?)_b(u)-(?)_b(u)| generated by the CFS method approximation and the error |(?)_b(u)-(?)_b(u)|generated by the statistical estimation respectively,and gives the analysis expression of the estimator error;the fourth part uses a large number of samples to verify the stability of the Gerber-Shiu function estimator under nonparametric statistics;the fifth part summarizes the main results of this paper and makes prospects for further research in the future.This paper innovatively applies CFS expansion method to the risk model with barrier dividend strategy,which provides a new research idea for nonparametric statistics of risk model with dividend.