Mortality Prediction Based On Fuzzy Lee-Carter Model And Its Application To Economic Capital

At the macro level,the year-by-year decrease of mortality rates is reflected in the continuous extension of life expectancy,which can have a significant impact on the solvency of the insurance industry.The pricing of annuity products by insurance companies is based on static empirical life table data,which inevitably has a lag in predicting changes in population mortality,resulting in inadequate pricing of annuity products in the early stages and annuity payment period in the later stages will far exceed expectations.If the insurance companies don’t take precautions,they will be unable to cover their expenses and fall into a serious solvency crisis.Therefore,a scientifically sound projection of future population mortality is vital to the sound development of the life insurance industry.Currently,the most widely used mortality projection model is the classical Lee-Carter model,which is a simple and practical mortality projection model that takes into account both age and time effects on mortality.However,the time series structure of the classical Lee-Carter model requires a high level of adequacy and accuracy of mortality historical data,while the short time span of mortality historical data and the scarcity of high-quality census data in China have made the classical Lee-Carter model unable to fully reflect the complex and diverse actual situation in China.Therefore,this paper takes advantage of the advantages of fuzzy set theory in dealing with uncertain data and fuzzy information to improve the classical Lee-Carter model.Firstly,after estimating the model parameters using the least squares method,the age-related parameters are processed into triangular fuzzy numbers to construct a fuzzy extension Lee-Carter model,and the optimal ARIMA time series model is selected to forecast the population mortality in China in the next 15 years.The fuzzy extension Lee-Carter model predicts the mortality results,and the left and right spreads increase as the confidence level decreases.Secondly,the article compares the central mortality rate predicted by the fuzzy extension Lee-Carter model,the prediction results of the classical Lee-Carter model with the actual mortality data in 2019,and assesses the advantages and disadvantages of the fuzzy extension model and the classical model using the model goodness of fit,mean percentage error and mean square error as indicators to test and prove the The validity and applicability of the Lee-Carter model were tested.The results of the study found that the improved fuzzy extension Lee-Carter prediction model compensated to a certain extent for the shortcomings of the traditional prediction model in terms of sensitivity to mortality changes,better solved the error problem caused by the poor quality of our data,and also reduced the requirement for limits on the error homoskedasticity.Based on the mortality projections,this paper uses economic capital to measure the longevity risk faced by insurance companies from the perspective of risk management.Taking an annuity product as an example,the mortality predicted by the fuzzy extension Lee-Carter model is used to calculate the TVa R value of the annuity product in order to measure the economic capital required for the annuity product coping with the longevity risk.The effect of changes in confidence level on mortality and economic capital is further investigated.The results of the study show that the fuzzy extension Lee-Carter model can better represent the trend of population mortality in China,and the lower the confidence level,the greater the uncertainty of mortality,and the higher the amount of economic capital required.Based on the mortality forecast,this paper measures the economic capital of an insurance company’s annuity product from the perspective of risk management.Taking annuity products as an example,the mortality rate predicted by the fuzzy extended Lee-Carter model is substituted into the annuity product pricing formula to measure the economic capital required for the annuity product to cope with mortality changes,and the impact of changes in confidence levels on mortality and economic capital is further examined.The results of the study show that the fuzzy extended Lee-Carter model better reflects the trend of mortality in China,and that the lower the confidence level,the greater the uncertainty of mortality and the higher the amount of economic capital required.