| This paper constructs a life and annuity joint insurance model with delay considering marriage.The existence of delay factor can alleviate the financial burden of insurance companies to a certain extent,which is beneficial to both the policyholders and insurance companies,[0,1-α]period,the insurance benefits paid will be paid at the end of the current year,otherwise,the payment will be postponed to β of the next year."Double randomness"(that is,mortality and interest rate are both random)is becoming a hot area of actuarial research.In terms of random interest rate,considering the different risk preferences of different families,we set N1 families to choose CIR Interest rate model,and the rest N-N1families to choose ARMA(p,q)The interest rate model calculates the expected value of the discount function.In terms of random mortality,based on the Lee Carter random mortality model,UDD hypothesis is adopted for the fractional age group,and the expression of mortality force is derived.In addition,in the joint insurance of husband and wife set up in this paper,the factors of divorce and the dependence of future life span of husband and wife are considered.The dependence of death rate of husband and wife is mainly based on two points:1.Joint disaster,that is,the probability of death of husband and wife at the same time in an accident or disaster is greater than that of two unrelated individuals;2.The effect of heartbreak,i.e.the death rate of widows is higher than the total death rate in a short period of time,and then gradually decreases to the total death rate.Considering the advantage of women’s innate emotion regulation ability,the decline pattern of heartbreak effect of men and women is not the same.Therefore,this paper uses Gauss curve and index function to fit the decline pattern of heartbreak effect of men and women respectively fm(t)=Ame-t2/2Bm+1,Among them,the deceleration of exponential function is greater than that of Gaussian curve,and the deceleration of Gaussian curve first increases and then slows down,reaching the maximum at t=Bm.The existence of the dependency of death rate of husband and wife makes the death rate of husband and wife not only depend on the current state,but also depend on the stay time of the current state The semi Markov chain can satisfy this point.Therefore,in this paper,the semi Markov chain including the five states of husband and wife survival,husband and wife survival,husband and wife death,husband and wife divorce should be used in the construction of two person random mortality model.Based on the expression of death force,the expression of transfer probability is givenThe joint insurance model established in this paper stipulates that:(1)If both husband and wife survive,the first i couple at the end of each year can get bi living annuity.(2)If one of the couple dies,the living party can still get ei of life annuity every year until the end of their life.If neither of the couple survive more than q years after insurance,they can get ci of compensation.(3)If the death time of the later death policyholder falls in the[0,1-α]time period of the year of death,the CIinsurance benefit paid shall be paid at the end of the year,otherwise,the payment shall be postponed to beta time point of the second year.(4)In case of divorce,the policy will be terminated and the premium paid will not be refundedFinally,the actuarial present value of the model is given under the condition of "double random". |
