Actuarial Model Of Four-element Family Life Insurance Under Random Interest Rate

As an important part of the financial industry,insurance plays an important role in risk management.However,compared with developed countries,the de-velopment of China’s insurance industry still has a long way to go.From another perspective,the development prospect of the insurance industry in China is still very broad.What’s more,life insurance is a significant category in the insurance industry,therefore,its research significance is obvious.With the aging of China’s population and the comprehensive promotion of the two-child policy,the status of the sandwich generation will become the norm situation for more families.When there was an accident in the main income member of the family,an insurance could provide the family with guarantee.And many family-based joint life insur-ance would become four people,so the research on the four-element family life insurance actuarial model could better help insurance companies to develop new products to meet the current needs of consumers,thus improving the companys’product competitiveness.In the traditional life insurance actuarial model,fixed interest rate is used to calculate the level premium.However,with the opening of China’s interest rate market,interest rates are also constantly changing with certain randomness as well.The changes in interest rate will have an important impact on level premium.If the interest rate rises,the calculated premium will be low.Although it could promote the sale of the policies,it was also difficult to compensate the insured.If the interest rate goes down,the calculated premium will be high.Then,the sales of the policies may not be good.In ddition,on the investment side,the asset allocation of the insurance company’s would also have an impact on its earnings based on changes in interest rates.Therefore,changes in interest rates will affect the profits of insurance companies and the life insurance actuarial model under random interest rates will be more reasonable.This thesis would use the stochastic process,mathematical statistics,insurance actuarial,the basic principles of interest theory and research results and practice from all over the world on stochastic interest rates as well as combine qualitative analysis and quantitative analysis,combine comparison and induction.Firstly,using interest theory and one-element actuarial model under fixed interest rate,deduct the actuarial model of the four-element joint life insurance under the fixed interest rate,especially the formulas of the joint-life status and the last-life status.Then,using the knowledge of the stochastic process,establish a double stochastic model of interest force(δ(t)= δt + β|B(t)|+ γN(t))consisting of the reflected Brownian Motion and the Poisson Process.Furthermore,the necessary assumptions are made for the policy,and the foue-element joint life insurance ac-tuarial model under the random interest rate is deduced to the formula for level premium.And use the latest life table provided by China Banking and Insurance Regulatory Commission to fit the survival functions,then introduce the formula of the dead force functions,and apply them to the actuarial model to have the sensitivity analysis of the parameters and the study the relationship between pa-rameters and level premiums.However,in addition to the level premium related to risks of life,the insurance companies’ pricing process also requires addition-al premiums that reflect their operating costs and profit levels.Therefore,in actual applications,adjustments need to be made according to the specific cir-cumstances of each company.Finally,the advantages and disadvantages of the model are summarized,and the future promotion and optimization of the model are discussed.