Research On Semiparametric Mortality Prediction Model With Cohort Effect

Research of population mortality has always been a core issue of demographics and insurance actuarial science.In recent years,with the rapid development of social economy and medicine in various countries,many countries and regions have shown the characteristics of declining population mortality and prolonged life expectancy,and the risks of longevity has also followed.In this context,the accurate prediction of population mortality is not only important for governments and regulatory agencies to formulate more scientific and reasonable pension plans,but also critical for insurance companies to design life insurance products and reserve reserves for new features and formulate relevant policies.For the prediction of population mortality,the random prediction model is more and more widely used.The random prediction model can fit the data better than the deterministic prediction model,and also has stronger fitting and prediction capabilities.Among the random mortality prediction models,the Lee-Carter model and the CBD model are widely used and studied.These models belong to the parametric model,which has many disadvantages such as unknown parameters and complicated estimation steps.In order to solve these problems,the use of non-parametric and semi-parametric methods to establish mortality prediction models began to attract people's attention,but there are few relevant research results.Li et al.(2015)set the traditional CBD model as a class of time-varying coefficient panel data model,and used the local linear method for estimation.Li et al.(2015)set the traditional CBD model as a type of time-varying coefficient panel data model and estimated it using a local linear method,while Li et al.(2019)further extended the linear relationship to polynomials.However,Li et al.(2015)and Li et al.(2019)did not consider the impact of the queue effect.In order to solve this problem,based on the above research,this paper proposes a type of semi parametric variable coefficient addable CBD model,which sets the effect of queue effect as a non-parametric part,so as to describe the queue effect more flexibly.The traditional mortality model,the traditional CBD model and the Lee-Charter model study the problem of age-specific mortality in multiple years in a region.However,in many practical situations,we have to consider the death rate in multiple regions,such as the study of the death rate of 31 provinces in China.In response to this problem,we propose a type of spatio-temporal variable coefficient model,and consider the effect of queue effect,and further propose a class of semi-parametric spatiotemporal variable coefficient model.At the same time,this paper also gives an estimation method for the proposed model,and analyzes the Italy morality data by this model.Based on practical problems,the paper applies the semi parametric modeling method to the construction of mortality prediction models,and proposes a new type of semi parametric mortality prediction model.The conclusions drawn will enrich the content of the mortality prediction research field and provide more scientific statistical prediction methods for relevant departments.