Penalty Function Optimized Mortality Prediction Model

Due to the economic development,the improvement of living conditions and the improvement of medical standards,the mortality rate of all ages of the population in China has decreased,and the average life expectancy has increased.It is estimated that around 2022,the proportion of the population over 65 in China will reach 14%,and will be transferred to the aging society.Compared with other countries in the world,China’s aging is not only fast,but also has a high proportion of the elderly population,resulting in the situation of "getting old before getting rich",which has a significant impact on China’s economic development and social stability.For individuals,the wealth accumulated during work is not enough to maintain the pension life after retirement.At the same time,China’s pension system is unbalanced,the dependency ratio of the elderly in various provinces and cities is increasing year by year,and the pension balance between provinces is unbalanced,so the government fiscal expenditure is facing great pressure.Mortality research is the basic work to balance the pension system and alleviate the risk of longevity.Accurate mortality prediction and life expectancy prediction can provide strong data support for the development of China’s pension system.In the study of mortality,Lee-Carter mortality prediction model is a widely used random mortality model,which has a good performance in China’s data.This paper establishes Lee-Carter model based on China’s mortality data.In the process of parameter estimation,weighted least square estimation and maximum likelihood estimation are mainly used.Due to the irregularity of the estimation result of the mortality change factor in the model,the resulting life table presents some unstable changes across ages,so it is necessary to adjust the parameter smoothly.At the same time,the life expectancy calculated by the two methods is significantly higher than that published by the National Bureau of statistics in the same period,and the estimated results have errors,which need to be adjusted in combination with the official life expectancy data.Considering the adjustment of the above two aspects,the constraint condition of parameters is added into the objective function as a penalty term,and the penalty function is expanded to achieve the effect of optimizing parameters.Considering the optimization mode of applying two constraints separately and at the same time,the estimation results obtained by different methods are compared.Finally,based on the weighted least square estimation method,the estimation method with two constraints can get more accurate results,and use the results to predict the future mortality and life expectancy in China.Considering that China’s pension system is a way of local co-ordination,there are significant differences in the level of economic development and life expectancy among provinces and cities,it is necessary to analyze the mortality situation in China from the perspective of provinces and cities.By optimizing the parameters of penalty function,the Lee-Carter mortality prediction model of each province is fitted to predict the life expectancy of each province.The four economic regions of eastern region,central region,western region and northeast region are divided to discuss the parameters and life expectancy of each regional model.At the same time,based on the future life expectancy of provinces and cities,this paper analyzes the impact of life expectancy extension on individual pension accounts and the impact of delayed retirement on enterprise annuity.Finally,based on the three pillars of China’s pension system and the national overall planning,the corresponding suggestions are put forward.