Research And Application Of Long-range Dependence Mortality Model

With the rapid development of global economy and the continuous improvement of living standard,the population aging of various countries tends to be accelerated.This change has brought great pressure to both government agencies and insurance companies.Future policy changes and insurance product pricing depend on accurate modeling of mortality trends.Therefore,it is of great significance to study mortality model.In recent years,some scholars have found the existence of long range dependence in mortality data.Based on the existing research results,this paper builds a long range dependence mortality model combined with fractional Brownian motion to provide a basis for the mortality modeling method.The main work is as follows:(1)Extend the Milevsky-Promislow model with fractional Brownian motion,propose the long range dependence Milevsky-Promislow model,and make fitting predictions based on individual mortality data in Italy.It is found that Milevsky-Promislow model with long range dependence has a good fitting effect.(2)As the long range dependence Milevsky-Promislow model is difficult to actuarially value,the simple Volterra Ornstein-Uhlenbeck model is used to directly model the intensity of death.Based on the related properties of affine Volterra process,the closed form solutions of survival probability and insurance product price are derived.(3)Compare and analyze the two models according to their discrete survival functions in long range dependence Milevsky-Promislow model and their closed survival functions in Volterra Ornstein-Uhlenbeck model.The results show that long range dependence has different effects on the two models.And although the long range dependence Milevsky-Promislow model fits survival curves better,Volterra OrnsteinUhlenbeck model calculates the value of retirement annuity more accurately.Based on the research results of the long range dependence mortality model,this paper puts forward reasonable suggestions for government agencies and insurance companies,and makes prospects for the improvement of the model.