Study On The Evaluation Of Life Insurance Reserve Under The Prediction Model Of Old Age Mortality

Many studies have shown that population aging is a problem that human beings must face.During the 14 th Five-Year Plan period,our country has made significant decision deployment to actively cope with the aging population problem.Among them,the life insurance industry will be the focus of development,and the life insurance companies should assume the corresponding social responsibilities.In the future,life insurance companies will be responsible for many old-age insurance policies,so we must consider how life insurance companies should do a good job in their own management under the trend of population aging.Therefore,we mainly analyze the impact of insurance policies of the elderly population on companies.As we all know,most life insurance companies now generally use fixed mortality and fixed interest rates to calculate the pricing of their products.In real life,our interest rates and mortality rates are constantly changing.In this way,life insurance companies will face interest rate risk and longevity risk and other problems.These problems reflected in the reserves of life insurance companies will lead to underestimation or overestimation,which will make the operation of insurance companies fluctuate.So,we need to use a dynamic stochastic model to talk about how the reserves of insurance companies change under different scenarios.In this paper,mortality model and interest rate model are screened first.Through comparative analysis,we will choose the old age mortality prediction model and Vasicek model for research.Lee-Carter model will also be used for comparative analysis.Firstly,we preprocessed mortality data from 1994 to 2020 and interest rate data from 2006 to 2020 by referring to previous studies.In terms of parameter estimation,weighted least square method and ordinary least square method are used for parameter estimation of mortality model,and generalized moment estimation method is used for parameter estimation of interest rate model.In terms of data prediction,we used the ARIMA model to predict the time series of the mortality model,and for the interest rate model,we used the Monte Carlo simulation method to simulate the interest rate data in the next 20 years for 10,000 times.After obtaining the corresponding mortality rate and interest rate,we set three scenarios for comparative analysis.Scenario A is fixed mortality and fixed interest rate pricing;Scenario B is the pricing of dynamic mortality and random interest rate obtained by Lee-Carter model.Scenario C is the pricing of dynamic mortality and random interest rate obtained from the prediction model of old-age mortality.Given our regulatory environment,we should set our prices to the best of our ability according to the regulations of the China Banking and Insurance Regulatory Commission.Only in this way can we truly reflect the operation of life insurance companies.Finally,we conduct reserve assessment for term life insurance and annuity insurance under the three scenarios,including the analysis of age,gender,insurance period and payment years.By studying the distribution of reserves obtained from many data,we can compare the changes of life insurance reserves under three scenarios and different types.The results show that the improvement of old age mortality has a significant effect on reserve.And older age,longer periods of insurance,and changes in payment patterns all make the effect bigger.This paper suggests that life insurance companies consider the impact of improved mortality at advanced age in their pricing and evaluation.