The Actuarial Model Of Quaternary Family Life Insurance Under The Conditions Of Dynamic Mortality And Stochastic Interest Rate

The study of joint insurance for quadruple families is becoming increasingly important as more and more families of four are expected to emerge as a result of the "two-child" policy.In traditional life insurance actuarial models,fixed interest rates and static mortality rates are often used as assumptions for rate setting.However,in reality,interest rates are constantly changing,sometimes dramatically,and as health conditions improve and the economy grows,people's standard of living increases,leading to an increase in average life expectancy and a gradual reduction in mortality levels at different ages.Therefore,it is not reasonable or scientific to use fixed rates and static mortality assumptions when setting rates for insurance products.As life insurance policies often have long coverage periods,the pricing assumptions of fixed interest rates and static mortality rates will also make future benefit liabilities more unpredictable and pose a huge potential risk to the continued operation of insurance companies.2020 is a crucial year for China to fight and win the battle against poverty and to achieve the goal of building a moderately prosperous society,and among poor families,many of them have two or even more children,how to help these low-income families who have been lifted out of poverty to solve the problem of returning to poverty due to the death of the main family workforce is a social issue that our insurance actuarial students should be concerned about.Considering the economic conditions of such families,the Quadruple Family Joint Term Life Insurance combines the advantages of joint insurance and term life insurance in a more "cost-effective" way,allowing them to obtain a higher amount of insurance at a lower premium,giving them a more comprehensive protection.In this paper,we use a stochastic interest rate model and a dynamic mortality model to simulate real-life fluctuating interest rates and improving mortality rates,and introduce dynamic mortality rates and stochastic interest rates into traditional life insurance actuarial models,replacing the assumptions of static mortality rates and fixed interest rates accordingly,to establish an actuarial model for quadruple joint life insurance based on dynamic mortality rates and stochastic interest rates,so as to obtain a more realistic and scientific pricing model The innovation of this paper is that it also incorporates the assumption of dynamic mortality and stochastic interest rates.The innovations of this paper include: introducing both the stochastic interest rate model and the dynamic mortality model into the actuarial model of life insurance,as previous studies have only focused on one of them but not both;considering the quadratic joint survival state,which is in line with the current trend of dichotomy;most studies have obtained actuarial models of life insurance with full continuity for the sake of convenience,but in reality,the payment of premiums and the payment of insurance benefits are This paper takes into account realistic factors,assuming that the benefit payments occur at 24:00 on the date of death and that premiums are paid at the beginning of each year;in order to be more realistic,the paper also examines gross premiums,making the conclusions of this paper more practical;this paper not only derives the model,but also carries out distribution simulations by means of Monte Carlo simulations to obtain the corresponding distribution properties.Due to the author's limited ability,there are some shortcomings in this paper: in the mortality data,except for the national census data,many years of data are population sampling surveys,which may lead to some errors in the data;the time factor in the dynamic mortality model has been decreasing in recent years with the improvement of living standards and medical and health conditions,but the author believes that it should stabilise at a certain point in time In this paper,the quadratic joint state assumes that the deaths of household members are independent of each other,but in reality,the death of a household member has a certain impact on the lives of other members,which in turn affects their disease incidence and even mortality rates;with the development of research,the dynamic mortality model and the random interest rate model have derived many more complex and scientific forms,but this paper does not This paper does not address and cite them.The first part of the paper is an introduction,which analyses the relevant policies and the overall development of the life insurance industry in China,explains the background and significance of the paper,and reviews the relevant literature at home and abroad in recent years;the second part briefly introduces the relevant models used in this paper,their parameter estimation and testing methods;the third part gives a brief description of the dynamic mortality model used in this paper--In the third part,the parameters of the dynamic mortality model used in this paper are estimated by the weighted least squares(WLS)method with the corresponding number of deaths,and then the ARIMA model is estimated to predict the time factor,and a series of tests are conducted to prove its validity.In the fourth part,the parameters of the Vasicek model,a stochastic interest rate model used in this paper,are estimated using the generalised method of moment estimation(GMM)to obtain significant parameters,and then the model is used to forecast future interest rates.In the fifth part,the dynamic mortality model and stochastic interest rate model obtained in the first two parts are introduced into the quadratic joint life insurance actuarial model to complete the initial construction of the model,and then the formulas for wholesale pure premiums,equilibrium annual pure premiums and equilibrium annual paid gross premiums are derived,and finally 10,000 stochastic interest rate paths are obtained through Monte Carlo simulation,and the distribution simulation of the established model is carried out to obtain the corresponding statistics and the nature of the distributions.The last part of the paper concludes that under the conditions of dynamic mortality and stochastic interest rates,the single premium,equilibrium annual paid pure premium and equilibrium annual paid gross premium of the quadratic joint life insurance actuarial model obey normal distributions and that the premiums obtained from the traditional actuarial model are underestimated,which can pose a significant risk to the ongoing operations of insurance companies.