The Actuarial Model Of Life Insurance With Stochastic Interest Rate

The insurance industry has now become the most important part in the financial field.For insurers,the discount rates of the company's future profits have a significant impact on its earnings,so it's necessary to estimate the discount rate reasonably which is directly related to the interest rate.This paper takes the influencing factors of interest rate into account and establish ARMA(p,q)model for interest force.The China's bond yields data is used for estimating the parameters and testing the model,which contributes to validating the rationality of stochastic interest rate model and fitting out the ARMA(1,1)model corresponded.For individual life insurance,the death payment,annuity payment actuarial present value calculation formula with the stochastic interest rate are given by the paper.Through the formula above,the net premium and reserve calculation formula of a variety of annuity insurance products are deduced.According to the calculation and analysis of the actuarial present value of the specific insurance products,it can be found that for the insurance company,the personal life insurance model under the stochastic interest rate reduces the profit risk caused by the shortage of the net insurance premium of the insurance company.In addition,it is more reasonable to estimate the different insurance policies based on the stochastic interest rate.The extraction of the liability reserve reduces the risk of the insurer's solvency in the future for the insured.For the dual life insurance,the paper mainly analysis the models for the situations of the joint survival and the final survival.When the two insureds' life are independent,the influence of different death forces is further considered on the basis of stochastic interest rate,and the calculation formulas of death payment and annuity actuarial value under four different death forces are given.When the two insureds' life are not independent,the corresponding calculation formula of death payment and annuity actuarial value is given according to the life function given by Frank Copula model and Common Shock model.This part of the actuarial model makes great significance for the dual life insurance,especially husband and wife life insurance product's development and evaluation.At last,the paper sums up the actuarial model of dual life insurance to the case of n insured persons.Furthermore,the formulas of life insurance actuarial calculation under different death order are given.Through the example of the joint life insurance of family members(father,mother and son),the actuarial present value of eight death situation are calculated,which is of practical value to the design and development of group insurance products of insurance companies.